Bafetimbi Gomis admitted to being flattered with reports linking him with a move to Liverpool and Chelsea, while saying he would be open to joining a club in the English Premier League.
Gomis is seen as a target for both Liverpool and Chelsea as the duo look to strengthen their attacking options.
Liverpool were the team to have reportedly made the first contact, but it is understood the Blues have moved up in the race for the French international striker.
According to Canal+, both clubs sent scouts to watch Gomis in action for Lyon against Paris Saint Germain over the weekend with tentative negotiations reportedly beginning between Lyon and the two Premier League clubs.
Lyon are keen to offload Gomis, to reduce their considerable wage bill, and it looks like it will be up to the 27-year-old striker to decide which club he will join in January.
"I'm happy, but if it is for my interest, and the three parties are okay and I can progress, then yes," Gomis told Canal+. "The interest is flattering.
"These are big names (Liverpool and Chelsea). But I do not pollute my mind with the idea of a departure. Anything can go very quickly in football."
Gomis has shown good form this season, scoring 10 goals in 17 games.
Meanwhile, Brendan Rodgers has revealed the club will not spend big in the January transfer window. The Liverpool manager said the Reds would definitely bring in fresh faces next month, but chances of big-name arrivals are slim.
"There is a bigger picture for sure and it goes back to affordability," Rodgers told the Independent. We will spend money in January to try and bring fresh faces into the group and give us that support at the top end.
"But the reality (about) all the names bandied about is 'are they going to be available?' Certainly we will bring in what we can help us and then we will revisit again.
"All our problems were never going to be solved in this window because the January window is one of the least productive and the least movement goes on there.
"But we will look to solve some of our problems then and then we will look to revisit it in the summer knowing that in the summer we will be better placed than the last previous summer."