The Leinster star underwent a procedure to repair a neck desk in May but there are fears he may not be fit in time for next month’s Rugby World Cup.
Reports last week claimed that Healy has experienced numbness and has been unable to make a fist after the operation.
Healy trained with the squad at their open day in Musgrave Park last week and Kearney reported yesterday that the Lions prop is being monitored on a weekly basis.
“Cian is coming on fine. It’s very much a week-to-week situation with him. So we just have to wait and see whether Cian is fit or not,” he told RTÉ.
“Everybody is training hard so fingers crossed we don’t pick up any more injuries over the next three matches.”
Kearney admitted the squad were devastated following the confirmation that Tommy O’Donnell’s hope of making the squad were ended by a horrific hip dislocation which marred Saturday’s win over Wales in Cardiff.
Kearney said: “He has spent two nights in hospital. The plan is that he will get home in the next 24 to 48 hours. He didn’t require an operation. He will have to keep the weight off it for the next six to eight weeks as he starts his rehabilitation.
“Fingers crossed he will make a full recovery in due course. He’s been in camp now for the last six weeks with 45 other players. They’ve become really tight and really close and to see one of their colleagues stricken down on Saturday was pretty devastating for everybody that witnessed it.
“It’s really unfortunate but at the end of the day it’s part and parcel of sport and Tommy is just really unlucky.”
However, Kearney was more upbeat when quizzed on Andrew Trimble’s well being.
The Ulster wing, who caught the eye on Saturday, was taken off late in the first half with a foot sprain.
“Andrew is going to have a precautionary scan this afternoon so we await the results of that and hopefully that will turn out to be okay,” said Kearney.
Meanwhile, Sam Burgess will make his England debut against France on Saturday with Stuart Lancaster insisting he has earned his place in the team after proving himself on the training field.
Burgess has been picked at inside centre for the first of the three warm-up Tests leading into the home World Cup just 10 months after completing his high-profile cross-code move from rugby league.
The 26-year-old is only under consideration as a midfield option, not at blindside flanker where he played his best rugby for Bath last season, and starts between fly-half Owen Farrell and outside centre Henry Slade.
Burgess is in World Cup contention despite failing to convince in the number 12 jersey at club level, but Lancaster insists the powerful Yorkshireman deserves his chance to argue his case for selection in the 31-man squad that must be named by August 31.
England took the unprecedented step of bringing forward their team announcement for the visit of France to Twickenham by 72 hours, a decision Lancaster explained was made due to the long build-up to the game.
Burgess and Slade are three of four uncapped players in the 23 with Calum Clark starting at openside and hooker Luke Cowan-Dickie featuring among the replacements.
A Goode (Saracens); A Watson (Bath), H Slade (Exeter), S Burgess (Bath), J May (Gloucester); O Farrell (Saracens), R Wigglesworth (Saracens); M Vunipola (Saracens), R Webber (Bath), K Brookes (Northampton), G Kruis (Saracens), G Parling (Exeter), T Wood (Northampton), C Clark (Northampton), B Morgan (Gloucester).
L Cowan-Dickie (Exeter), A Corbisiero (Northampton), D Wilson (Bath), D Attwood (Bath), J Haskell (Wasps), D Care (Harlequins), D Cipriani (Sale), Billy Twelvetrees (Gloucester).