Gibson was part of United's Carling Cup winning team earlier this month, but has yet to make an impact at Premier League level.
Reports claimed Fulham boss Roy Hodgson was showing an interest ahead of a potential end-of-season swoop for the Republic of Ireland international.
However, Gibson has brushed off the speculation and has no plans to bring an end to the learning process at Old Trafford.
Really happy"I never heard anything (of the Fulham interest)," he said in the Irish Examiner. "But I am really happy where I am for the minute.
"This season I have been involved a lot more than last season or the season before.
"I've learned about how Man United play and about how the manager works."
The 21-year-old has made two substitute appearances in the Premier League this season and is eager to be more involved in Sir Alex Ferguson's plans.
He added: "It is the next step for me. I am pushing at the moment, but I haven't really got my chances.
"Hopefully I can push a bit more in the next few games and get my chance in the league."