Sow's talks with the French side over a new deal has broken down and the Senegal international's current contract is due to expire in 2013.
Sow has admitted he would be interested in a move to a 'big club' like Arsenal.
"I have a contract signed until June 2013 and Lille want me to sign another contract but the negotiations have stopped," Sow told RMC Sports.
"I don't accept the conditions or the silence from the club. That's not me putting on pressure, just the truth.
"I'm only thinking about football and it's not possible to leave in January.
"But my dream is to play in the Premier League, because you progress as a player with the atmosphere, goals and game.
"I watch the games with envy on TV. I desire to play there one day. Arsenal are a big club. But we will see."