It was reported earlier that Strauss's move to Pretoria was a done deal, but business interests in Bloemfontein now look likely to keep Strauss at the Cheetahs, Beeld reports.
According to the supersport. com website, the Cheetahs also significantly upped their offer for Strauss and he told the website that he'll make a final decision on his future this week.
Should Strauss not go to the Bulls it would be a setback for the union as they are set to lose the services of Bongi Mbonambi, who will leave for the Stormers after growing tired of sitting on the bench.
Bandise Maku and Callie Visagie are the other hookers in the Bulls squad.
The Bulls may lose out on Strauss, but it appears a done deal that two of his team-mates at the Cheetahs, prop Trevor Nyakane and Lappies Labuschagné, will head north to Loftus Versfeld.