Dragons flanker Taine Basham is the only player who has been released from the Wales squad to play for one of the four Welsh regions in the United Rugby Championship this weekend.
Dragons have a back-row injury crisis, with Basham’s return giving them three specialists for their trip to Ulster.
No Scarlets, Cardiff or Ospreys have been made available.
Wales will lose England-based Dafydd Jenkins, Nick Tompkins, Tommy Reffell and Dillon Lewis, plus Will Rowlands.
Jenkins, Tompkins, Reffell and Lewis will not play this weekend because there is no league action but World Rugby regulations stop them from training with Wales all week.
Lock Rowlands’ club, Racing 92, play Bordeaux Begles in the French top 14 on Saturday.
Scarlets trio Gareth Davies, Kemsley Mathias and Joe Roberts, Cardiff forwards Seb Davies, Teddy Williams and Evan Lloyd and Ospreys centre Owen Watkin were not involved in the matchday 23 that lost 31-7 to Ireland last weekend in Dublin.
Dragons duo Leon Brown and Cai Evans have been struggling with injuries, while Cardiff lock Davies has a slight back problem.
Ospreys travel to play Edinburgh on Friday night, while Dragons go to Ulster the following day.
Also on Saturday, Scarlets face a trip to Connacht and Cardiff host Leinster.
Wales want to keep 28 players training with the national squad before the final two Six Nations matches.
Wales, who have lost their three games in this year’s tournament and suffered 10 defeats in the last 11 Six Nations games, host France on 10 March with Italy visiting Cardiff six days later.
