Bowe was last night ruled out of the tournament opener against Italy at Stadio Flaminio on Saturday week with no date set for his return.
But any hope the 26-year-old Lions winger will be fit to face France a week later faded today following an update from the Ospreys' head physio Chris Towers.
"We're continuing to liaise with the Irish medical team regarding Tommy's condition and the management of his injury," said Towers.
"We've taken the decision to continue to offload him, allowing the knee to settle further, and at this stage remain optimistic that the problem will resolve in the short term.
"We are hopeful that in a couple of weeks, if he continues to improve as he is, he will be able to get back into some rugby specific training without any reaction or ill effect.
"The signs are encouraging at this stage, but it is clear that it will be another couple of weeks before we can confirm whether or not this problem will impact on more than just the first couple of Six Nations fixtures."
Ireland's preparations for the Six Nations have been hit by an injury crisis that has robbed them of eight players capable of featuring in the matchday 22.
Head coach Declan Kidney can ill-afford to lose such an effective player as Bowe for the first two games of the championship, especially with three of his potential replacements - Shane Horgan, Geordan Murphy and Andrew Trimble - also injured.