Selected by Chancellor Angela Merkel's conservative Christian Democrats and her junior coalition partners the pro-business Free Democrats, the Lower Saxony state premier is widely expected to be voted into the ceremonial post following the surprise resignation of Horst Köhler last month.
But the opposition's dark horse candidate Joachim Gauck has garnered more support from the public and even some politicians from Merkel's coalition parties have voiced their preference for the former East German civil rights activist.
On Friday Wulff told daily Ruhr Nachrichten that he saw no connection between his likely election and the stability of Merkel's coalition.
But the presidential candidate did say that he could not rule out that “the capacity for the government majority would be discussed in the public if their own candidate were not elected.”
Wulff also encouraged the coalition, weakened by internal bickering over several policy issues, to find a way to cooperate.
But the new candidate said he would rather have former President Köhler, who resigned over criticism of comments he made about Afghanistan, still in office.
“He was highly competent and an idea generator,” Wulff told the paper. “He had a high rate of acceptance among the people. It's a shame.”
Köhler's successor will be chosen on June 30 by the Federal Assembly comprising member of parliament and representatives of the 16 German states.