The 24-year-old has been one of the Premier League's stand-out performers this season, helping the Clarets all-but secure survival with two games of the season to play.
The ex-Manchester United youngster had played every minute of every top flight game this term before missing the draw with West Bromwich Albion last weekend, consistency which saw him make his international debut in March and nominated for the PFA Young Player of the Year award.
But The Mirror understands that Liverpool manager Jurgen Klopp has made Keane his priority defensive signing this summer in order to cure the Reds' problems at the back. The Anfield club have shipped 42 goals at the wrong end this season, with no club in the Premier League's top seven possessing a worse record.
Having made close to 700 appearances for Liverpool across 17 seasons, Jamie Carragher knows what it takes to build a stubborn defensive unit in the top flight. However, the club legend believes a move for Keane would be ill-advised, given he does not represent an improvement on current first choice central defensive pair Dejan Lovren and Joel Matip.
"I like him, I think he's had a really good season," Carragher said of Keane on Sky Sports. "It's a big jump to go from Burnley to Liverpool and a completely different way of playing. That 4-4-2 at Burnley, it's a lot of protection, and maybe a similar thing to what we're seeing with Mamadou Sakho at Crystal Palace.
"He looks a completely different player there but he's playing a completely different game. Jurgen Klopp was talking about centre-backs at top clubs a couple of weeks ago. The questions asked of you are completely different. If you are going to buy Michael Keane, it's going to be £25m. He's a young English player.
"Is he better than Lovren and Matip? He's maybe the same level. If you're spending £25m on a centre-back he has to go straight in your team and make a massive difference. I don't think he is quite at that level to come in and make a massive difference."