Tiatia steered Dragons to only their second victory of the season in last weekend’s 22-14 Challenge Cup win over Newcastle.
Speaking to the South Wales Argus, external, Blumberg said a decision over Tiatia’s position would be made at the end of January.
“The intention is to try and keep Filo in post and make sure it works out for him,” said Dragons chief executive Rhys Blumberg.
“He is capable and doing a good job. Both parties are working well together and it’s been a good start.”
Blumberg added Dragons are not actively seeking a new head coach to replace Flanagan, but would be ready if the former Ospreys back rower Tiatia did not want to continue in the role.
“It will either be that Filo is in position as head coach for the next two years or that he is returning to being defence coach, with X as head coach after we have made an offer and had it agreed,” he said.
Tiatia, 53, was not drawn on whether he would be interested staying as head coach, but said: “I’m learning as we go; these young men are growing and are surprising me in a lot of ways.
“Their motivation becomes mine because I really want them to succeed as well. We just have to take it day by day, keep learning.”
Tiatia will next lead the side when they take on east Wales rivals Cardiff next Thursday in the United Rugby Championship [URC], with a bumper Rodney Parade crowd expected for a festive fixture the Dragons have not won in 10 years.
However, they will do so with injury problems at lock with Steve Cummins and George Nott both ruled out following head collisions in the win at Newcastle. Wales hooker Elliot Dee could return for the fixture.
“It was a scary moment with George, but he did well post-game and was walking around,” he said. “We are following protocols and just making sure both athletes are safe to return.
“Cardiff are a good. We’re really looking forward to it, we’ve watched them closely and it’s a great opportunity for the players to represent the club really well.”