JULY 27: Cabinet spokesperson Bandula Gunawardena told reporters on Tuesday that Mr Rajapaksa was not in hiding but the date of his return was not known.
The former leader fled Sri Lanka after mass unrest over an economic crisis.
Many protesters say he mishandled the nation's finances, leading to soaring prices of essential goods.
Mr Rajapaksa left Sri Lanka on 13 July for the Maldives, before making his way to Singapore on 14 July.
He submitted his resignation shortly after his arrival, which was formally accepted by the Sri Lankan cabinet on 15 July.
The former president travelled with his wife and two bodyguards. He no longer has legal immunity as a head of state.
Singapore says the ousted president did not ask for political asylum when he arrived.
Mr Rajapaksa had been initially granted a 14-day visa for his stay in Singapore. But that has now been extended another 14 days, Singapore local media reported on Wednesday.
Speculation has since swirled about his possible plans, with some suggesting he might move to the United Arab Emirates.
However Bloomberg quoted an unnamed Sri Lankan official as saying Mr Rajapaksa was keen to return to Colombo.
"To my knowledge he is expected to come back," Mr Gunawardena told reporters on Tuesday.
Sri Lankans blame Mr Rajapaksa's administration for their worst economic crisis in decades.
They have been struggling with months of daily power cuts and shortages of basics like fuel, food and medicines.
Mr Rajapaksa has been replaced as president by his close ally Ranil Wickremesinghe - he was voted in by lawmakers last week but is deeply unpopular among Sri Lankans.