Everton and Ipswich played out a 2-2 draw in the penultimate game at Goodison Park, with Moyes side giving up a two-goal lead.
The 22-year-old started but was hooked off in the 68th minute having failed to make a significant impact for the now relegated Tractor Boys.
Speaking to the press ahead of the game, Moyes all but confirmed that his side are hoping to sign Delap but admits it will be hard to beat Chelsea and Man United to his signature.
The Scottish manager said: "He would be one who we would certainly have an interest in. I think what he probably has to look at will probably be bigger than what we are. So, we would certainly be interested if he was interested in us. That’s for sure."
Delap has a £30 million release clause in his contract that became active once Ipswich were officially relegated.