The Sun says Grant will throw the keeper back into the fray after losing back-up Carlo Cudicini for the season.
Chelsea initially feared the Czech international would be out for the season but the keeper has come safely through several weekend training sessions.
The stopper will still have the stitches in the cut on his chin but he is keen to return to action after missing Chelsea's last 10 games though injury.
Grant has had the all-clear from the Chelsea medical staff and will select Cech for tonight's must-win home game against struggling Wigan.
The Chelsea boss was reluctant to discuss Cech's prospects yet admitted: "He is improving all the time. He still has the stitches in his face but he has been training, in one session with a protective mask and in another without it.
"The injury does not stop him talking or communicating with his defenders."
He said: "Carlo will be out for around four weeks and there is a possibility he could miss the rest of the season."
Chelsea's only other alternatives are third-choice keeper Henrique Hilario and 18-year-old rookie Rhys Taylor from the youth team.