The Stirling-born forward, who has been one of the leading performers in the BBL so far, was on a short-term deal after joining from the Spanish club Manresa in the summer.
After leading Britain to their only Olympic victory, over China, Achara attracted interest from club sides in Germany and Spain.
Although the 29-year- old has yet to finalise an alternative employer, he will consider other options after failing to agree on a permanent switch to the Emirates Arena.
"My temporary contract is up and we couldn't reach agreement on a deal for the rest of the season," he said. "I'm now going to have to look seriously at potential moves back overseas."