Kalas, who is the longest-serving player at Stamford Bridge, has been on loan at six clubs since signing for Chelsea in 2010 and he is ready to leave the club this summer as his contract has just two more years left to run.
Now 26, Kalas enjoyed one of his best loan spells yet in Bristol alongside fellow Blues loanees Jay Dasilva, who has an option to buy in his deal, and Kasey Palmer.
The centre-half, who has previously had stints at the likes of Fulham and Middlesbrough, made 38 appearances in the Championship for Bristol City as they finished eighth in the table, missing out on a play-off spot by four points.
The Czech Republic international has 19 caps for his country and he posted a teasing message on his social media accounts as interest from Bristol City and other Championship clubs mount.
"Now it is time to relax and after that back to business and where? Who knows," Kalas said on Instagram .
Bristol City are targeting up to seven signings to help Lee Johnson get the club into the Premier League as the second-tier club outline their ambition.
Chelsea have long been keen to offload several loanees this summer, despite having a transfer ban imposed on them by FIFA for what they believe is wrongdoing in the signing of under-18 overseas footballers.
Specifically, the Blues have moved to sell their older talent and have put option-to-buy clauses in the contracts of their older loan stars, including the likes of Tiemoue Bakayoko, Mario Pasalic, Kenneth Omeruo, Victorien Angban and Ola Aina.
However, several loanees will also get their chance next season due to the transfer embargo with a Japanese visa being secured for Mason Mount due to the club's pre-season matches in Asia.
Charly Musonda and Baba Rahman are set to return but they could leave the club again either on loan or on a permanent deal.