The Welsh international damaged knee ligaments when playing for Wales in a warm-up game with England, ahead of the Rugby World Cup in 2019.
The 27-Test veteran wrote on his Twitter feed, 'Enjoying some time back in the middle, not far now @ospreys.
One report from Swansea, where the Ospreys are based, said Anscombe, 30, was looking the part in his return.
"His quality has been evident to all, and he has massive presence in the way he conducts himself. For a young player like Josh Thomas, to have Gareth around, and Stephen Myler as well is huge.
"Gareth's been out a long time, so it's a case of not overdoing it and working at the right pace. But the signs are promising," the report said.
The injury he suffered could not have occurred at a worse time. He had played first five-eighths in four of Wales' five Six Nations games during the Grand Slam campaign earlier in 2019.
He had been working in tandem with Dan Biggar under coach Warren Gatland's lead.
He has been named in the Ospreys squad to play a pre-season friendly with Northampton on Friday.
Former British & Irish Lion and Wales wing Shane Williams believed if Anscombe could regain his form, some interesting decisions await Wales coach Wayne Pivac.
Apart from Biggar, Rhys Priestland has returned to Wales while other players who could contest the first five-eighths role include Rhys Patchell, Callum Sheedy and Jarrod Evans.
In his Rugby Paper column, Williams said that Anscombe was a player the Ospreys and, to a lesser extent, Wales needed desperately.
"But I must make my opinion clear that we cannot rush Gareth back into action too quickly. To do so would be criminal," he said.
While Williams said he had never suffered serious injury in his career, he found it difficult to imagine what it would be like to miss two years of play.
"I do know what it is like to miss months of action. It is an awful experience.
"You are constantly worried if you are going to come back as the same player, and there are worries over losing your place both a regional and Test level.
"Gareth will have experienced all those emotions. It must have been very tough, which is why it would be criminal to throw it all away now," he said.
Williams said the goal for Ospreys is to work Anscombe back in with some play before Christmas.