He also claims new boss Andre Villas-Boas must secure a Champions League place in his first season at the club.
"I was bemused by what happened to Harry because he had done such a fantastic job at Tottenham, taking them from the bottom of the table and into a Champions League position," Lineker told the Daily Star Sunday.
"I wonder how much further the team can go without massive investment but that is their challenge. Are they really going to challenge for the title?"
He added: "They sold one of their best players again during the summer and you don't see teams winning trophies doing that."