The two Premier League sides are believed to be keeping a close eye on the 19-year-old's situation at Schalke, with City supposedly ready to make their move this January.
Schalke have so far been adamant they have no intention of selling the winger, but Sane's father would not veto a move to England if the opportunity arose.
"Of course it makes me proud to see my son catch the attention of big clubs with his good performances," Sane senior told Bild.
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"He knows I am always there for him if he needs my advice. We talk a lot.
"But Leroy is an adult and old enough to make his own decision on what he wants. He knows that I will always support him."
Sane has a contract with Schalke until June 2019.