The Scotland international’s future at Anfield was thrown into doubt earlier this month after the signing of Joe Allen from Swansea City with rumours gathering that he would leave the club in the coming weeks.
A move across Merseyside to the Toffees has been touted with David Moyes in search of a new midfielder after selling Jack Rodwell to Manchester City whilst Fulham have also been linked.
However Adam insists he has no plans to quit the Reds just a year after joining from Blackpool and is prepared to fight for his place in the starting lineup.
“I have never heard anything about Fulham, nobody has spoken to me about it, so for the moment it is paper talk and at the moment I am not going anywhere,” Adam told the Scotsman.
“I am happy at Liverpool and why would I leave after a year? There is no point. I am open enough to say I have had a conversation with the manager but for me I’m not going anywhere.
“I am playing with some of the best players in the world, I have a good coach, good manager, and I am learning every day from what he is doing.
“I want to play this year and hopefully I get the opportunity to do that. It is a big season for everybody.
“For us at Liverpool it is a big season, we have got Europa League and we want to improve on what we did last year in the league.”
Adam faces a tough task to seal a place in Rodgers’ starting eleven this term with Allen, captain Steven Gerrard, Lucas and Jay Spearing ahead of him in the pecking order.