He has started only two games in the SPL during his time at Parkhead and has been linked with Wigan and Wolves.
But, after scoring the winner against Morton in the Scottish Cup on Tuesday night, McGinn outlined his desire to spend a long time as a Celtic player.
"If there are clubs in England showing interest in me, it means I must be doing something right," the 22-year-old told the Scottish Sun.
"I was at Swansea for a week before Celtic showed an interest in me. Once Celtic came in for me though, I jumped at the opportunity.
"Roberto Martinez was the Swansea manager at the time and, of course, he's at Wigan now.
"Swansea actually had me watched for months and showed massive interest. Maybe Martinez is still keen on me.
"I grew up supporting Celtic and my priority is to get in the team as soon as possible. I see myself here for the next five or 10 years, I'm loving it so far."