Graham has moved on loan from Sunderland to Blackburn until the end of the season, and he has made a good start at the Championship club.
The 30-year-old netted his third goal in his last six appearances for Rovers in a victory over Birmingham City last Tuesday.
“I’m happy here and I’ve stated that," Graham said, when asked whether the move could become a permanent one in the summer.
“I just want to concentrate on my football but I’m sure the gaffer will sit down with my agent and maybe talk about what is going to happen in the summer and we’ll take it from there.
“I can [see a future here]. I’m enjoying my football, which I’ve not said for a long time now, and that’s the most important thing for me at my age.”
Graham has proven to be a prolific finisher in the Championship previously, and he has quickly endeared himself to the Ewood Park faithful.
The experienced forward’s move to the Stadium of Light never worked to much success, though.
Graham scored just one Premier League goal for Sunderland in 37 appearances, and he never managed to secure his place in their starting line-up.
It seems likely that he will be made available for sale in the summer, and if he keeps up his current form at Blackburn, there are set to be plenty of admirers.