Ullrich withdrew from the Swiss Cycling Federation last Thursday, thereby invalidating his Pro Tour licence.
But Massak has announced that he would be prepared to help the former Tour de France winner get his career back on track following allegations he was implicated in the Operacion Puerto doping scandal.
"If Jan moves to Austria, then I will grant him a professional licence," Massak said.
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"Until now, all that has been written in the media and the press is speculation, and that's an unacceptable situation. It cannot be that Ivan Basso gets acquitted in Italy, Ullrich gets hammered in Switzerland and that an enquiry is opened against Jaksche in Austria that is immediately thrown out due to a lack of evidence."
In order to qualify for membership of the Austrian Cycling Federation, Ullrich would have to declare his main residence as being in Austria.
After leaving the Swiss Federation, Ullrich confirmed that he had been in contact with other federations.
Even if he was to acquire a new licence, the 32-year-old would still need to find a new team, as he was sacked by T-Mobile in the wake of the blood doping scandal that broke on the eve of this year's Tour de France.
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