Former England boss Keegan claims Chelsea’s stance defies logic considering the 34-year-old’s contribution to the club’s success.
He told The Sun: “Like most people, I don’t get it. You begin to think there must be something else going on that we don’t know about.
“Lampard’s 34, so I certainly wouldn’t be giving him a three-year contract if I was manager.
“But if he wanted a one-year rolling deal or something like that, for me it’s a no-brainer.
“The clubs think differently, quite obviously, but people will be queuing up to sign Lampard.
“Make no mistake about it, no one is going to be offering him a three or four-year deal.
“The best way to do it is to give a one-year deal, then either the player or club can move on if they’re not happy.”