Morgan has captaincy experience at international level.
Having missed the Six Nations and summer tour through injury, it remains to be seen whether he regains the Wales leadership role.
Morgan and Dewi Lake were Warren Gatland’s 2023 World Cup co-captains.
Hooker Lake then led the side on this summer’s trip to Australia.
After giving Morgan the Ospreys captaincy, coach Booth has recently indicated he would give the national role to Lake, partly based on what he describes as less competition at hooker.
Morgan says he is concentrating on trying to get back into the Wales squad for the autumn internationals against Fiji, Australia and South Africa.
“I’m just hoping I’ll be back on the field with the Ospreys and performances can take care of themselves and I can get back in the Wales squad,” said Morgan.
“That would be brilliant. Dewi is a great leader and captain himself. He’s done a wonderful job in the summer and a lot of the boys said so.”
Morgan is fit to start the season after missing most of the last campaign because of knee and hamstring injuries.
The 24-year-old had been one of the leading World Cup performers but was unable to build on his breakthrough on the global stage.
“It was frustrating and tough going into the injury group, especially after the World Cup,” said Morgan.
“I was looking forward to coming back to Ospreys, having a good run of games and seeing how the rest of the season would go before picking up an injury just before Christmas.
“It was a lot harder than I probably thought it was going to be, but I am now looking forward to the start of the season.”