MADRID (Reuters) - Spain's market regulator on Monday cleared Hochtief takeover bid for toll road company Abertis, starting a one month period in which Hochtief and rival bidder Atlantia can improve their proposals.

However, both Hochtief, owned by Spanish builder ACS, and Italian motorway and airport operator Atlantia said last week they were in talks over their competing bids and a source said they could decide to break up the company in a move to prevent a bidding war.

If a deal is reached, Atlantia would likely withdraw its offer for the Spanish company and sign an agreement with ACS on how to divide Abertis's assets, the source said on Thursday.

Atlantia and ACS are in talks over a possible joint bid that would mean joint ownership and avoid a breakup of the company, El Mundo reported on Monday citing unnamed sources close to the talks and adding an agreement could be reached sometime this week.

At Friday's closing prices, Hochtief's offer values Abertis at around 18.2 billion euros ($22.4 billion) while Atlantia's offer values it at around 17.1 billion euros, including Abertis treasury shares.

($1 = 0.8112 euros)

(Reporting by Paul Day; editing by Sonya Dowsett and Jason Neely)