The Gunners midfielder sustained the injury during last Saturday's 1-0 loss to Newcastle, causing him to sit out the midweek match against Inter Milan.
Rice was included in Lee Carsley’s England squad for Nations League games against Greece and Republic of Ireland, despite being unable to train this week.
Reports suggest the former West Ham United star has been unable to even get a boot on the foot where he has suffered the break but is still prepared to push through and play on Sunday at Stamford Bridge.
Arsenal have failed to win in their last three Premier League games with their Champions League defeat to Inter adding to their woes.
The Gunners have slipped to fifth place in the Premier League as a result, level on points with Chelsea ahead of their Sunday showdown and seven behind league leaders Liverpool.
‘Declan unfortunately picked an injury against Newcastle,’ Mikel Arteta said earlier this week.
‘He was able to finish and he wasn’t feeling good the last few days. We’ll have to assess him on Thursday and see if he’s ready for Chelsea.’
Should he come through that game unscathed, Rice is also ready to play for England in those forthcoming international games against Greece and Ireland.
Mikel Merino and Thomas Partey started in midfield in Rice’s absence in Italy with the Spain international involved in two first-half penalty incidents.
Inter were awarded a penalty in controversial circumstances when the ball struck Merino’s arm on the stroke of half time, a decision that infuriated Arteta after his side saw their own penalty appeals turned down 15 minutes earlier.
Merino was ‘punched in the head’ by Inter goalkeeper Yann Sommer as he rose to meet a cross. The midfielder was substituted at half-time shortly after.
‘He was not concussed,’ Arteta explained. ‘But yesterday and today he was already not feeling great. After, when I looked at him, I decided to take him off because I need him 100%.’
Martin Odegaard meanwhile made his return off the bench in injury time in Italy following a three-month layoff with an ankle injury.