It is believed they have approached the Austrian outfit with a £3 million bid for Mbombo, who is the cousin of Manchester United superstar Romelu Lukaku.
They face stiff competition from English Premier League side Burnley, along with Italian clubs Napoli and Sampdoria.
The 23-year-old is expected to leave Rapid this summer as they look to cash in on their asset.
Meanwhile, Celtic manager Neil Lennon has told Arsenal they will need to pay significantly more than £15 million to land Tierney.
The Gunners had a bid rejected a few days ago but are expected to return with a second offer.