The Red are seen as top contenders to sign him, who scored 12 goals for relegated Ipswich in the Premier League this season.
The former Liverpool defender believes Delap would be an upgrade on Rasmus Hojlund but says a move to Manchester United is too soon, suggesting Everton as a better fit.
"I don’t think Delap should go to Man United. What happened to Hojlund, sometimes when you’re going from a team who have been relegated - I know Man United are 16th, but they are one of the biggest teams in the world, with the eyes and ears on them. I think that’s such a big step. I know people might say it’s not in terms of league position, but Man United are a monster,” Carragher told Sky Sports.
"I do think he’s an upgrade on Hojlund, but I almost think that next step should be Everton or something. You know you’re going to play every week, you’re going to be the main man, you’re going to feel like one of the best players in the team.
“He’s the best player in the team at Ipswich, everything goes through him, so go to another club where you’re that for two years, then go to Man United or wherever. A team playing in the Champions League or trying to compete at that sort of level."