Although the 32-year-old's contract with the Blues expires only in 2016, the Czech Republic international may want to leave Chelsea a little sooner due to him falling behind Thibaut Courtois in manager Jose Mourinho's pecking order.
Some reports in Italy have indicated that Roma are interested in signing Cech during this transfer window, however Mourinho has quashed down all the rumours, insisting that there is "no chance" of the 32-year-old leaving Stamford bridge in January especially now that their other goalkeeper Mark Schwarzer has joined Leicester City.
Cech's agent Viktor Kolar also revealed in December that it was unlikely that his client would be leaving Chelsea in the January transfer window.
"It's unlikely Petr will leave Chelsea in the January transfer window. The club and coach want to keep him to help win the title," Kolar told the Telegraph.
Due to this reason, Arsenal boss Arsene Wenger, who is reportedly a big fan of Cech, having attempted to sign him Rennes before he moved to Stamford Bridge in the summer of 2004, is reportedly prepared to patiently wait until the summer before making a move for the 32-year-old, according to the Telegraph.
Apart from Arsenal, Liverpool are also looking for a new goalkeeper following the poor form of Simon Mignolet this season.
However, it is unlikely that Mourinho will be willing to sell Cech to a Premier League rival like Liverpool and Arsenal.
Still there is a possibility of the two Premier League clubs changing Mourinho's mind as he did sell Juan Mata to Manchester United for £37 million last January.
Wenger is desperate to sign a new goalkeeper after growing frustrated with his current first choice Wojciech Szczesny, who was recently fined for smoking in the showers after the Gunners' New Year's Day defeat at Southampton.
The 24-year-old Polish goalkeeper has been in poor form this season, and this has forced Wenger to assess his goalkeeping options for the remainder of the season.
The Gunners do have David Ospina, who was signed from Nice at an undisclosed transfer fee in the summer, but the Colombian goalkeeper is relatively inexperienced to be Wenger's first-choice stopper.