Pearce also insists the former Arsenal trainee, who is a transfer target for Premier League newcomers Burnley, will remain on the banks of the River Trent even if he does not put pen to paper on an improved deal.
Forest have turned down a bid from Burnley for Lansbury, 23, who still has two years remaining on his existing contract.
"At this moment in time I think we are very, very close to agreeing a contract with Henri to extend his stay," Pearce told the Nottingham Post. "Beyond that, even if he does not sign the new deal, he will not be leaving the club. I want him here.
"The one thing with Henri, which I have noted over the last week or so, is that he does have a smile on his face.
"I think he has looked around that dressing room and seen the quality he is surrounded by - and I think he has been buoyed by that.
"I think he will be happy here, without a doubt. And that is important. That is the bottom line. I don't want anyone here who is doing me a favour.
"We can't do that. The team is too important, more than any individual. We want Henri to stay here and fight for his place.
"I think he is very close to extending his contract, this week. From there, he will be back in action next week as well."
Lansbury has been out with a knee injury sustained during pre-season but he could return as early as Tuesday night when Forest travel to Bournemouth.
Pearce added: "If he does not play on Tuesday then he will definitely be part of things on Thursday (in a behind closed doors friendly). We will take it from there, really."