His father who is Sri Lanka's High Commissioner in London and a President's Counsel is also reported to have left for Singapore this morning (December 26).
Deputy minister Mushtapha is expected to return to the country on Monday (December 29).
There is speculation that both Mushtapha and his father would back Common Opposition Presidential Candidate Maithripala Sirisena on their return from Singapore.
Recently Mushtapha had threatened to quit the government if the controversial Bodu Bala Sena (BBS) movement supports President Mahinda Rajapaksa at next month's election.
Early this week the BBS announced it will support the President.
Both Mushtapha and his father have appeared at court cases involving the government.