UFC welterweight champion GSP, who had been sidelined through injury for some 18 months, made his comeback on Saturday night, defeating interim champ Carlos Condit in the main event of UFC 154 in Montreal.
St-Pierre impressed as he recorded a decision win, and speaking afterwards, White confirmed he would give the Canadian two weeks to recover before looking to discuss his next fight.
And although GSP has refused to commit to fighting Silva, White is confident it will happen.
"It's the No. 1 best pound-for-pound fighter in the world against the No. 2 best pound-for-pound fighter in the world," he toldFox Sports.
"It's a big fight.
"We think people want to see it, and we think the guys want to do it, so we'll do it. They will fight, and it will probably be in May or around May.
"[St-Pierre] is lumped up. He's sore. He feels like he just got hit by a bus, I'm sure. He hasn't fought in 18 months. I'll make this fight.
"We're going to sit down with Anderson, probably in the next two weeks, and I'm sure we're going to sit down and talk to St-Pierre and his team, too.
"Who knows? Maybe we go into this thing, and St-Pierre says, 'Absolutely not,' but I just don't see that happening."