This story has been reproduced from today's media. It does not necessarily represent the position of Liverpool Football Club.
Liverpool scouts had been keeping a close eye on Lyon's striker Bafetimi Gomis in recent weeks as Rodgers looks to strengthen his attacking line without breaking the bank, but the deal may have to wait as the previously out of favour striker has said he is happy to stay until the summer.
The club had been pushing the 27-year-old towards the door, even agreeing a fee with Rubin Kazan in the summer but a frank discussion with coach Remi Garde and a hands-on part since the birth of his child in September have helped the €15m man find a new lease of life.
"Is it my best start to a season? Yes. The fact I became a dad has a lot to do with it. I'm full of the joys of spring, and it helps my football," Gomis told the club's website.
The strong number nine, who has been likened to Didier Drogba, has been linked with a move to a number of clubs but Liverpool were thought to be closest to signing him after representatives from Merseyside travelled to watch his hat-trick performance in a 4-1 win over Marseille two weeks ago.
A ten goal start to the season is the first time Gomis has shown the sort of form that encouraged Lyon to dig deep to secure him from their great rivals and weekend opponents St-Etienne in 2009.
"Even if we never know what can happen in football, I fully intend to stay in Lyon until the end of the season," he said. "I planned until the end of December but I think the coach is quite pleased with me. He pushes my limits.
"Overall, we had a frank discussion. He was not happy with me and told me that I could do more."
Gomis' contract expires at the end of next season, and the Lyon chairman says that they will listen to offers for him then.
Liverpool boss Rodgers has also been linked with a January move for Aston Villa's Darren Bent and Chelsea's Daniel Sturridge.