Bovis Home Groups has approached Galliford Try in recent weeks in a bid to reopen discussions about a merger, which previously broke down two years ago.
Bovis is keen to combine a large proportion of their operations, according to Sky News.
A deal would be a move toward the consolidation of Britain's housebuilding sector, with two of the UK's ten biggest housebuilders combining.
The market value of Bovis is just over £1.3bn, while Linden Homes owner Galliford is worth around £550m, with a merger between them increasing their stock market value to around £2bn.
How close the two are to agreeing a deal is unclear, a source told Sky News, while Bovis are thought to be uninterested in taking on Galliford's construction sector, which was responsible for a recent profit warning from the company and could be sold to a third party.
Galliford said earlier this week it would cut up to 350 jobs in its construction arm as it tries to streamline its business.
The approach from Bovis is a reversal of what happened in 2017, when Galliford tried to take over its previously smaller rival.
Any offer from Bovis is likely to be in shares, sources told Sky.
Bovis and Galliford Try both declined to comment on Saturday.