The England international has had an inconsistent season at White Hart Lane and could be offloaded this summer for £15 million.
Sources close to Tottenham suggest Redknapp is fed up with Lennon's inability to follow directions, factors that could lead to a move to Liverpool.
“Harry feels Lennon is not learning, not improving and not listening to instructions,” a Tottenham source told Goal.com.
“He has been really disappointed by Lennon’s performances since the first half of last season and does not believe he is as willing to run at the full-back as he should be.”
“They have a really bad relationship and Harry wants to cash in,” said the source.
“Spurs have not yet started touting him around but if they get a good offer, they will probably sell him.”
With Gareth Bale also close to departing the club, and Real Madrid and Inter Milan among others ready to bid for the Welshman, Tottenham could lose two influential players during a summer where they were expected to build a squad capable of challenging for the Barclays Premier League title.
Liverpool meanwhile have put a winger at the top of their transfer wish list and Damien Comolli, who is set to lead negotiations for transfer targets this summer, is a known admirer of Lennon from their time together at Spurs.
Kenny Dalglish is likely to have to choose between Lennon and his international teammate Ashley Young, who has long been tipped with a move to Liverpool as well.