Dee, 30, missed the end of last season and the summer Tests against South Africa and Australia but was expected to return at the start of this campaign.
Dragons head coach Dai Flanagan says Dee, who has played 51 Wales internationals, suffered a “little setback” and is not expected back until December.
Young Cardiff hookers Evan Lloyd and Efan Daniel, who both toured Australia, are struggling with injury, their captain Liam Belcher is definitely missing, and Ospreys number two Sam Parry was out of favour in the summer.
With Dewi Lake and Ryan Elias the experienced hookers available to Gatland, young Dragons front-rower Brodie Coghlan, 23, could be an another Wales option after impressing for the Dragons at the start of the season.
“We would be ecstatic if any of our players gets picked but probably more so with Brodie given the work and effort he has put in,” said Flanagan.
“Not long ago he was up in [North Wales regional team] RGC on loan fighting to be a professional rugby player, but it’s one step at a time for him.
“We didn’t necessarily think we would see this level of impact but what we did see was somebody who took his job very seriously over the summer.
“He changed his body shape, reflected on what he needed to do physically, and you can see a very fit player.”