Ozil, who has Turkish family roots, sparked controversy last May when he was photographed with Erdogan, raising questions about his loyalty to Germany on the eve of their disastrous World Cup campaign.
He quit the national squad soon after, accusing German football officials of racism.
Bild did not disclose the wedding date in the report which stated Ozil wants Erdogan to attend as his witness.
The reported invite drew sharp criticism in Germany, whose government has been sharply at odds with Ankara over a range of human rights questions in recent years.
“I think it’s inappropriate,” German politician Cem Ozdemir, whose parents are Turkish, told Bild on Sunday.
“Everyone is allowed to invite who they want to their wedding,” he said. “That also obviously applies to Mesut Ozil, but former and current national team players are also role models.
“They must ask themselves if they live up to that role, when they give themselves up to autocrats, who enrich themselves at the expense of their country and make dissenters disappear into pits.”
Ozil has dated Gulse since 2017 and the couple announced their engagement in June 2018.
The Arsenal midfielder, a third-generation German, sparked controversy when he was pictured alongside Erdogan last May, raising questions about his loyalty to Germany on the eve of their disastrous World Cup campaign in Russia.
Criticism intensified after the red-faced defending champions crashed out of the first round of the World Cup.
In the wake of the World Cup fiasco, Ozil announced his resignation from the national squad citing “racism and disrespect”, aimed partly at German Football Association president Reinhard Grindel.