He played the first 45 minutes of the 3-0 victory at Stevenage Borough on Monday night, before making way at half-time in a tactical reshuffle which saw Rigobert Song replace him for his first match of the pre-season campaign.
Laurent says that he hopes his club Toulouse - who, having already been relegated, were dropped down a further division this summer by the French authorities because of financial irregularities - will let him go on a 'free' and explains: "I hope it will all be done this week; we are just waiting to hear from Toulouse to see what their position is.
"They can not ask for too much money, if anything at all, because they are starting again from zero.
"We will see what happens but it is beginning to drag on a bit.
"I would like to be a Hammer for good.
"Glenn told me I must fight to get a place in the 16 - and that is what I intend to do."
Laurent insists that he can adapt to the rigours of life in the Premiership - and the heat.
"The training is a lot different; it is more physical, but I am enjoying it, and the temperature is just like France!"
And he feels that West Ham have the players to make a serious challenge for Europe, adding: "It is a very good team and I think we can make the top seven."
"Glenn is a very good manager who talks very well to the players."
The Hammers boss himself adds: "I thought he did well again on Monday and he would be an interesting addition to the squad.
"Being a naturally wide left player he gives us another option, and hopefully we can do something with his club shortly."