The Londoner, who remains in Washington DC, is close to finalising a deal after receiving a qualifying offer last month from the Toronto Raptors.
British Basketball officials have confirmed that they have all but ruled out paying the cost of insuring Mensah Bonsu to play in Poland next month if he remains without a contract, a sum understood to be around £100,000.
However the GB star, speaking on Saturday, declared: "There's one thing that everyone doesn't have to worry about. I will be playing with GB this summer for sure, I just dont know when."
The ex-Hackney junior could arrive as soon as Wednesday for this week's friendlies with Spain and Lithuania in Seville.