Suarez, who arrived at Anfield in January 2011 from Dutch side Ajax, has been the Reds’ talisman so far this season and notched 11 goals in 16 appearances after signing a fresh long-term contract during the close season.
But speculation has suggested that Roberto Mancini and City were impressed enough to make a move for the forward – an idea that manager Rodgers dismissed out of hand on Thursday.
"He's certainly not someone we want to sell or move on. He has 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.
"We'll 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 you've seen up until this point, he's in a great moment in his footballing life here at Liverpool. He's scoring goals and working well.
"I'll just continue to communicate with all the players and Luis in particular. He is very, very happy here. There will be no bidding war. He is staying here."
The Reds’ No7 has struck 32 goals in 68 appearances for the club, having found the target on three occasions to help Uruguay reach the semi-finals of the 2010 FIFA World Cup South Africa™.