Tsipras wants reforms to achieve debt restructuring and to get Greece into the European Central Bank's quantitative easing program. Doing so may appease austerity-jaded Greeks by persuading them that years of financial sacrifice are paying off.
Energy Minister Panos Skourletis, who opposes some key privatizations demanded by lenders, including selling a stake in Greece's PPC power company, was among the ministers who could be replaced, one source said. Finance Minister Euclid Tsakalotos was expected to keep his post, the officials said.
Asked to comment on a possible reshuffle, government spokeswoman Olga Gerovassili told Skai TV only that the government's aim was the "flexible, fast, effective" management of the country.
A reshuffle would be testament to Tsipras's delicate balancing act between implementing painful bailout reforms and boosting his leftist Syriza party's popularity ratings which have been sagging for months. Syriza is trailing the conservatives.
He was first elected 21 months ago promising to end years of austerity for Greece, imposed by international creditors. But he was forced to reverse course by the prospect of the country being kicked out of the euro zone and pursue deeper reforms under a third international bailout. He was re-elected in September last year.
"If he (Tsipras) needs a cabinet which can conclude the review as swiftly as possible then a reshuffle would indeed ease the points of contention," said one of the sources, adding that it could happen as early as this month.
A second official said Tsipras has been mulling the move for some time but has not made any final decision, while a third official said a reshuffle was not expected to be broad but would affect the structure of ministries.
Another bailout review, which includes unpopular labor reforms, fiscal issues and privatizations, started in Athens on Friday. Tsipras had scheduled meetings with his European counterparts in Brussels to discuss the review.
Under its third aid program of up to 86 billion euros agreed in 2015, Greece pledged to press ahead with state asset sales to raise 14 billion euros by 2022 to cut public debt.
Athens is already off schedule in privatizing PPC. The state, which now owns 51 percent of PPC with a market value of 684 million euros, was expected to hire advisers in September to sell 17 percent of it. This has been pushed back for November, a privatization agency source said.
As recently as last Tuesday, Skourletis said the utility would not be sold under his watch. "It would be a disaster," he told Antenna TV. "That won't happen."
In an effort to boost popularity, Tsipras has taken on the country's broadcasting "oligarchs" - which the left wing widely views as corrupt and part of an establishment responsible for Greece's malaise - but the move has so far failed to lift its poll ratings.
In a poll conducted by Alco polling agency for newsit.gr last week, Syriza garnered 15.1 percent of support versus 21.5 percent for the conservative New Democracy party.
The attempt to reduce Greece's number of TV stations could also backfire.
One of the country's highest administrative courts, the Council of State, is expected to rule next week whether an auction on TV licenses launched in September is legal.
This may determine if Tsipras's closest aide and adviser, State Minister Nikos Pappas, who has been overseeing the auction would move to another ministry, one of the sources said.
"The licences project could turn into a disaster instead of a success story," another source said.