The Uruguay international has struck 11 goals across all competitions for the Merseyside outfit so far this season, on his way to becoming the Premier League's joint-top scorer alongside Robin van Persie.
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Rodgers remains reluctant to even consider letting him leave, though, particularly given the club's lack of depth up front and, when asked whether Roberto Mancini was serious about signing the player, the Liverpool boss was on dismissive form.
"You'll have to ask Roberto Mancini. If we lost Luiz then we've got no strikers, so I don't think I want to lose anyone," Rodgers told reporters.
"He's certainly not someone that we want to sell or move on. He's been a brilliant player to work with and we want to add to our squad, not take people out of it. Especially a world-class player."
When asked what chance the club had of holding onto their prized asset and Rodgers was bullish, pointing out that the 25-year-old recently signed a new long-term deal to keep him at the club until 2018.
He added: "We just continue to work and stay focused on what we're trying to achieve.
"Luis has already shown in the summer his commitment to the club. He signed a new deal and I think you've seen up until now, this point, he's at a great moment in his footballing life here at Liverpool.
"He's scoring goals and working well, so as I said I'll just continue to communicate with all the players and Luis in particular.
"As I said he's very very happy here. There will be no bidding war, no. He's staying here."