The 29-year-old signed a pre-contract with Saints in January but has now had a change of heart - citing family reasons for wanting to stay in the Highlands.
However, St Johnstone - who host County on Sunday in the Clydesdale Bank Premier League - insist they will not back out of the deal and are demanding a fee of around £200,000 from Brittain's current employers if they want to keep hold of the midfielder.
But Adams insists his club will not pay and admits Brittain may still end up elsewhere next term
The Dingwall manager is now waiting on the player to resolve the issue with St Johnstone but claimed a breakdown in communication with Lomas had stalled those efforts. He said: "We understand that Richard has tried to get hold of Steve Lomas a number of times but has been unable to do that."
Under employment law, Brittain's contract with Saints is signed and sealed although his registration remains with County until the end of the season.
The Staggies blocked Saints' attempts to take the player south earlier this year when they rejected a £50,000 offer.
Now that Brittain has changed his mind, however, Saints will now insist on a fee before they release him from their agreement - but Adams said: "We have stated that we will not be paying any transfer fee if he was to come back to Ross County.
"The latest is that St Johnstone and Richie are talking at this point in time. I'm sure there will be a conclusion very soon. We will wait and see what happens but it is in Richard and St Johnstone's hands now. The player has stated he doesn't want to go to St Johnstone so St Johnstone have got a problem now about what do they do."
With County's reluctance to cough up for their own player, Adams concedes Brittain may yet move on. "It's a difficult situation," he admitted. "Richard had already stated that he wanted to leave Ross County and move to St Johnstone for a better offer than he was on here. But we haven't offered him any terms to stay, we can't do that."