Michael Gove will allow EU nationals living in the UK at the time of the referendum to apply free of charge for citizenship if he becomes PM.
The Brexit-supporting environment secretary, who is running to replace Theresa May, will make an “open and generous” offer, sources said.
A Tory rival, International Development Secretary Rory Stewart, promised a “listening exercise” on Brexit.
So far, nine Conservative MPs have said they will contest the party leadership.
The official race gets under way in early June, after Theresa May stands down – but jostling between candidates has begun. The winner, expected to be named by late July, will also become prime minister.
Sources close to Mr Gove, one of the leaders of the Leave campaign