Police confirmed on Monday that a 35-year-old male pedestrian had been involved in a collision with a lorry on the A64 near Bishopthorpe, York, leaving him with serious injuries.
The man was airlifted to Leeds General Infirmary, while reports in the British media named Carlisle as the pedestrian involved.
Carlisle is the former chairman of the Professional Footballers' Association and the organisation have offered its support to him and his family.
Carlisle's wife Gemma took to Twitter on Tuesday to thank everyone for their well wishes and later provided an update on his health.
"Clarke's very poorly but he's alive and stable," she wrote.
"Best Christmas gift we as a family could wish for. Thanks again."
The former defender clinched promotion to the Premier League with Burnley in 2009, and the club's media manager Darren Bentley revealed they would show a gesture of support during the Boxing Day fixture with Liverpool at Turf Moor.
Bentley posted on Twitter: "To confirm, the club has been contacted regarding 1 min applause for Clarke Carlisle in 5th min on Boxing Day. We are happy to support this."
