With results going their way on Tuesday, Leeds overtook Russell Martin’s side in the table – but Saints do hold a game in hand on their promotion rivals.
The two sides will meet at Elland Road on the final day of the Championship season on what could prove to be a crucial game.
Ainsworth, who was sacked from his role at QPR in October, believes one particular Leeds player may hold the key.
Speaking on a Sky Sports soccer special programme, he said: “A couple of guys (on the panel) fancy Southampton with the run they have been on.
“I think Leeds are such a good side. If they can keep (Crysencio) Summerville in the form he is on, then he is this player.
“(He is) one that teams have had in the past where you say that player got them promoted. That player was the one.
“Summerville has done that. I will put my neck on the line and say Leeds will just pip it.”
Only three points separate Leeds, Saints, and Ipswich Town in the table, while Leicester City extended their lead at the top by 12 points after the midweek fixtures.
