Derby County, Wolverhampton Wanderers, Sheffield Wednesday and Nottingham Forest were reportedly interested in the Hibernian striker.
Cummings has been at Hibernian his entire professional career so far and has a contract until June 2017.
The 20-year-old is one of the best and most promising young forwards in the Scottish Championship.
Stubbs, though, seems confident that Cummings will not leave the Scottish Championship outfitat the end of the season.
The Hibernian boss has also revealed that the club have offered the Scotland Under-21 international a new contract.
“If it’s just Bristol City watching Jason, I’m surprised,” Stubbs told The Scottish Sun. “He’s obviously doing very well. He’s still got 16 months left on his contract.
"We’ve offered him a new one and we’re still hopeful he will sign it. I am very comfortable about it. If it does come to a situation, he’s worth a lot of money.”
January transfer window interest
Cummings has been in brilliant form all season and was linked with a number of clubs in the January transfer window.
The Daily Mail reported in December of interest from Championship sides Sheffield Wednesday, Burnley, Brighton & Hove Albion and Leeds United in the young Scotsman.
In January, The Daily Mail claimed that Nottingham Forest were interested in the Scotland Under-21 international, while Sky Sports reported of Wolverhampton Wanderers’ interest in Cummings (click here to read more) and The Sun linked the youngster with Derby County.