Rodgers, speaking at Melwood ahead of Saturday’s home match with Wigan, was asked about reports in Thursday’s papers suggesting City are looking to bid £40m for the Uruguayan.
“There will be no bidding war. Luis Suarez is staying here,” said Rodgers.
“He is certainly not anyone we want to sell or move. We want to add to the squad.
“We continue to work on what we want to achieve, Luis has already shown his commitment to club in the summer he signed a new deal. He is scoring goals here and working well.
“He is very, very happy here.”
Suarez signed a new “long-term” contract at the club this summer.
Meanwhile, Rodgers also explained that Lucas Leiva has returned to full training this week. “Lucas will come back into training, which is great news. He has worked tirelessly in his rehabilitation, so he comes back out onto the field in a good moment,” explained the boss.
“He won’t be ready to play for the weekend, but certainly over the next couple of weeks he’ll be very close.”