Aggregate Holdings SA is weighing a bid for CA Immobilien Anlagen AG, according to people familiar with the matter, potentially challenging U.S.-based Starwood Capital Group for control of the Austrian property group.

The real estate investor expressed interest in December in acquiring Starwood Capital’s near 30% stake in CA Immo and was rebuffed, the people said, asking not to be identified discussing confidential information. It is now considering approaching other shareholders with an offer, the people said.

Starwood Capital is on the cusp of triggering a 34.44 euros-per-share offer for the remainder of CA Immo, which will value the group at 3.4 billion euros ($4.1 billion). Run by Barry Sternlicht, Starwood Capital has been betting on CA Immo’s prime German office space and its big land bank in the capital Berlin and other German cities since buying its initial stake in 2018.

Aggregate is wholly owned by investor Guenther Walcher and already has exposure to property in Germany, including through its stake in Adler Real Estate AG, a landlord with links to Austrian businessman Cevdet Caner. Late last year, Aggregate sold 500 million euros in bonds in part to help fund future acquisitions, according to one prospectus.

Any move for CA Immo could prove difficult given the size of Starwood Capital’s holding and because the U.S. group owns so-called golden shares that allow it to appoint supervisory board members.

Discussions are ongoing and Aggregate could still decide against making an offer for CA Immo shares, according to the people. Representatives for Aggregate and Starwood Capital declined to comment.