Arsenal have fallen out of the title race after an abysmal run of form since the turn of the year.
Winterburn told Sky Sports how the summer transfer window will have to be a busy one for manager Arsène Wenger.
"He's going to have to look at his squad and realise it's obvious he has to go into the transfer market, and re-strengthen," Winterburn said. "There will be one or two players leaving anyway.
"You could say that Arsenal will need to bring in five or six players, but I just don't see them doing that."
The Gunners dropped more points in the Premier league at the weekend, drawing at home to Crystal Palace, and once again the same frailties have reared their ugly head for Wenger's men.
Arsenal have not been solid enough defensively or clinical enough in front of goal to be involved in the title race and these must be two key areas that the Frenchman has to address over the summer if they are to compete at the top level.
The money is certainly there to spend - they have the largest cash reserves of any club in world football, with £159 million sitting in their account, as reported by The Sun.
As Arsenal fans know all too well, however, whether Wenger spends it or not is another issue entirely.
Arsenal host West Bromwich Albion on Thursday night as they look to consolidate their Champions League spot.