A report in one newspaper on Monday suggested that Lazio and Chelsea would be in for him at a price of around £5m, and stated that he 'craved a move to Italy.'
It also said that ' he has gone missing in games or developed mysterious injuries'.
But Paul MD Aldridge insists: "He is our vice-captain and we are certainly not looking to sell him.
"This another non-story as far as we are concerned; we have received no enquiries about Paolo whose efforts, like everyone else at the club, are being devoted to Saturday and the need to finish our home games with that all-important win.
"And of course Harry is looking to strengthen our squad, not weaken it, this summer."
As for Paolo himself, he says: "I'm proud and honoured that West Ham say this story is rubbish: I feel like the West Ham shirt is part of my body."
Paolo is unhappy about the 'mysterious injuries' jibe and says: "Let's close this story about not playing games away; people can say I am crazy or stupid - but not that I will give up.
"I am not a whinger but now it is important that people know why I haven't played my best football in the last few months.
"I had a sinus infection and there is no story more clear than my situation: at the end of the year I'm going to have an operation on my nose.
"Ges, the doctor, and I know this problem, but I still play without saying anything to the supporters because I want to find strength inside myself and not go out and say 'sorry I played bad because of a sinus infection, I had a big problem with my Achilles tendon' - but this is the truth.
"Now, I want to tell the people because I don't want the people to think I didn't play well or wasn't consistent as the paper said.
"In the first six months I was one of the best players on the pitch, and everyone was talking about me in a fantastic way, saying we can't play without Di Canio.
"After December I started to have this problem again, this sinus infection and four weeks ago I got a problem - which I still have - with my Achilles tendon.
"In different circumstances a player might take time out but I didn't do this because I dedicate myself completely to this club.
"When we are saved I can try and find the problem and solve it once and for all because I want to play better than, not this year, but last year, when I did very well; I know I can do this.
"Three times I have had a sinus infection and played under antibiotics for two months.
"I am a man, not a robot; I am human and it is normal not to play 100% when conditions are not perfect.
"Just when I was coming back I started to have a problem in my Achilles tendon so I have been very unlucky in the last four months.
"But I didn't want to cry to the people about it because it is not in my character but now people will have to understand.
"I was ready to play at Aston Villa but the doctor told me not to travel; what is strange?
"I have been in bed with a temperature of 39.5 degrees; why is it normal when it is someone else but something strange when it is me?
"I played at Manchester United when I scored and we won, and at Sunderland when we won.
"I have played at the top level for the last 15 years; do you think that people say AC Milan, Lazio, or Juventus are going to buy you if you are scared?
"This is a stupid story and they have to stop; finish with this s*** once and for all.
"Okay, when they write about Di Canio it is big news, so I am happy for them that they are putting bread on the table.
"But sometimes I hope that they are a little bit professional and not only writing rubbish.
"If they want to put us - as a team - against each other, they are very wrong because we are a unit even if we know we didn't play very well this season.
"We will make sure we don't commit the same mistakes next season because we want to do the right things for the West Ham supporters.
"I will play on Saturday once again without training a lot this week because of my Achilles problem, even if the people are angry because Di Canio is not playing like six months ago.
"I want people to know that I have not lost my passion; it is because I can't train like six months ago.
"Anyway, apart from the last two games I have played well, creating chances for the team - even without training I've still been amongst the best.
"It is mathematical that I have been playing 30% below my quality, but if people think I am going to give up they are very wrong - I won't give them this opportunity.
"When we are safe I will stop because I want to look after my body and think about next year - but if we don't save ourselves this weekend I play on.
"I love to renew every week the love of the supporters because I have to deserve it.
"Harry knows that I need an operation with my nose but I told him I want to help him first, especially as we have a few players out.
"Then I will have it - I think this is a professional attitude; I want to stay with my team mates.
"It's not a bad operation but they have to open my sinus canals because I have an infection, so I need to get the oxygen through better.
"They will put a tube up my nose and take away all the infection.
"I have played the last two months with a big headache especially when it is cold - I feel pain in my eyes after half an hour.
"On Saturday I was in pain, and every game has been cold in the last two months.
"As I say, I am not a whinger - but it has been a real problem."