Extending the run to three clean sheets in a row would represent the best run of the season - currently West Ham have gone three hours 40 minutes without conceding, and Glenn says:
"That is the way forward; any team that wants to do well will only do it on the back of keeping clean sheets, but those two are in the past and we are only worried about keeping a clean sheet on Saturday," he says.
"We have worked hard on our defending and the two full backs have done extremely well, which has helped the centre backs concentrate on their game and so both Repka and Pearce are having a very good time at the moment - and that has got to continue in these last eight games.
"I include the goalkeeper in the relationship with the back four; he has done a lot better just recently, that has helped his confidence, and I am sure he will continue to do that for us."
He says he can't afford to worry about other teams - with Birmingham hosting West Brom at noon - adding:
"100% concentration has to be on getting three points against Sunderland; Bolton don't play until Monday and there is nothing we can do about what Bolton, Birmingham, or anyone else do.
"The only result we can affect is the one we are involved in and for us that is the game against Sunderland.
"I have always remained strong in my beliefs that come May we would have pulled ourselves out of the bottom three; there is still an awful lot of hard work to do but I have every confidence and large amounts of trust that we will be able to do that."
West Ham beat Sunderland earlier in the season when it was Howard Wilkinson's first game in charge - ironically his predecessor Peter Reid is now Leeds boss for the rest of the campaign - and this is Mick McCarthy's first away game since taking over.
"Mick is a very honest, hardworking manager and I am sure the players, once they get to know him and his players, will respond to Mick.
"He has been given a fantastic opportunity at a very big club.
"This is Sunderland's third manager this season and you have to be surprised, but I am very much against commenting on other clubs' affairs and you have to respect the decisions taken by each individual club.
"I played against Mick many times and we managed against each other when I was at Watford and he was at Millwall.
"He is big honest guy, a straight talker and, during the World Cup, which was very difficult for him, he handled himself really well - he came out of it with a lot of credit as a person.
"We know Sunderland are battling for their lives, for their Premiership survival, and also to impress their new manager again.
"It was a tough game up there, Howard Wilkinson's first, but I think we deserved to win; as the 1-0 suggests it was a tight game but we had the edge throughout.
"Now we entertain them in the hope that our supporters create the same atmosphere that they did at kick off time against Tottenham and we get off to a good fast start.
"The crowd has been good all season considering everything, but they were special against Tottenham and the lads really appreciate that level of noise and support.
"And of course we had the same at Goodison Park last week when they never stopped singing for the whole 90 minutes, and though we weren't exactly hanging on in the last few minutes, we were aware of the support and I am sure that helped us to keep strong until the final whistle."