Fulham and Stoke City are interested in Gayle, who scored six Premier League goals last season.
United manager Rafa Benitez is not interested in selling Gayle – and the striker’s keen to stay at st James’s Park.
Asked about speculation over his future, Gayle said: “I’m loving it here. My family’s all set. For the time being, if the gaffer’s happy with me, I’m happy at to stay.”
Benitez wants to bring in another striker to compete with Gayle and Joselu.
“Of course, we want to improve the team, and I understand that we’re going to bring in other players to improve the team,” said Gayle.
“It’s all part of football. It happens, and you have to prove to the gaffer that you’re the right person to start.”
Gayle – who netted in the club’s 3-0 win over Chelsea on the final day of last season – wants to make a bigger contribution up front this coming season.
“It’s important that we kick on now, stay focused and start the season on the front foot,” said the 28-year-old. “Personally, I want as much gametime as I can get, and I want to improve on my scoring.
“The gaffer obviously has confidence in me to do a job, and hopefully I can continue that.
“The opportunity’s there for me. The gaffer’s given me every opportunity to prove myself. Last season, perhaps I didn’t get as many goals (as I wanted), but I was getting opportunities.
“If I continue to get those opportunities, I will score goals. Hopefully, I get the chance to prove myself again this season and I do myself proud.”
Gayle won the penalty converted by Christian Atsu in Tuesday night’s 2-0 win over Dublin side St Patrick’s Athletic.
“The fact that the boys are finding me in the positions I want to be to score goals is important for me,” said Gayle.
“I just need to improve on my touch and finishing, and hopefully I can continue that through pre-season.”