Knill, who has one-year remaining on his contract and has been offered a new deal by Bury, played for Swansea between 1987 and 1989.
He insists that such talk has only come about because of the rapid progress that has been made at Bury since he joined the club 18 months ago, and Knill remains firmly fixed on finishing the job he has started at Gigg Lane.
"It is nice to be linked with jobs like Swansea but it is just speculation which has come about because I am a former Swansea player and because Bury did really well last season," Knill told the Manchester Evening News.
"Swansea is a big club with great potential and that is a really big job. I am ambitious but I have not been at Bury for long and I am not at a point in my career where I am looking to move to another club.
"I want to finish the work that I have started here and, hopefully, I will get the time to do that. I have been offered a new contract. I am thankful for that as it shows that the board think that I am doing a good job here and I am currently mulling it over."