Byrne picked up the injury in the Six Nations against Ireland though is no longer wearing a protective boot.
He said: "I'll give anything a try to make that game so I'm having a few sessions in the tent. It's different but hopefully it will help."
Byrne hopes to rubber stamp his place as front-runner for the British Lions No15 jersey by helping the Ospreys to their first European semi-final.
Ian Gough also looks set to recover in time but Gavin Henson it out with his third injury this season.
Scott Johnson clocked on at the Ospreys on Monday but coach Sean Holley insists he is still in charge for Europe.
Former Wales boss Johnson arrived at the Liberty Stadium at the weekend to take up his post as director of coaching after a year in charge of USA Eagles.
But Holley will call all the shots ahead of the crunch cup tie in Limerick. He said: "Scott will take some time to soak up the environment and see what's going on before he steps in. I doubt he will have any input this week ahead of Munster."
He added: "Scott will be instrumental at the Ospreys. He will bring a new voice and fresh approach as well as his confidence."