The Daily Express says Walcott has a sponsorship deal with Nike, the sports company Garry Cook left to become executive chairman at Manchester City.
Cook was president of Nike's Michael Jordan brand and will be well aware how profitable Walcott could be to City, on and off the pitch.
Following the Abu Dhabi takeover, City boss Mark Hughes has almost limitless funds to strengthen his squad.
"If the right player is attainable, then we have the means to pay a bit extra," said Hughes. "But we are still looking for value. We are still looking for good, young players who will gain in value."