Jean Charest is thinking about running to replace Andrew Scheer as federal Conservative Party leader, according to sources close to the former Quebec premier.

Those sources told Radio-Canada, CBC's French language service, that Charest is consulting with his family.

Charest hadn't seriously considered a leadership run until several caucus members and former MPs reached out and urged him to do so, according to sources.

The sources said Charest is being drawn toward the leadership race by his focus on a number of issues facing the country right now, including national unity, the environment and Canada's place on the international stage.

Charest served as a minister in Brian Mulroney's cabinet and later served as leader of the federal Progressive Conservatives when they were down to just two seats in the 1990s.

He left the federal scene in 1998 to join the Quebec Liberal Party, eventually serving as premier between 2003 and 2012.

If Charest does formally enter the ring, he'd be a controversial candidate.

For years now, Quebec's anti-corruption squad, known as UPAC, has been investigating the Quebec Liberal Party's financing during the Charest period.

Sources told Radio-Canada Charest is aware of the pall that investigation could cast over his candidacy, but maintains he did nothing wrong.

The next step in the leadership contest is for the Conservative Party's National Council to form a leadership election organizing committee, which will decide on the rules, procedures, process and timelines for the contest.

After weeks of beating back criticism over his election performance, Scheer announced last week he will step down as leader once a successor is chosen.