The controversial former Chelsea chairman, 73, is understood to have offered the money to become part of a takeover at Elland Road being made by Sebastien Sainsbury, according to the Independent.
Sainsbury is the only remaining bidder still involved with Leeds and talks between Sainsbury and Whites chairman Gerald Krasner are ongoing about a £25m buy-out with the next round of talks scheduled for tomorrow.
Bates and Sainsbury were seen lunching together at The Dorchester Hotel in London last week.
According to one source, Bates told Sainsbury he would invest £10m in Sainsbury's consortium in exchange for 51 per cent of Leeds and the role of chairman.
"Ken said he had one more footballing adventure in him," the source said. "He's absolutely serious about it."
Bates stepped down as the chairman at Stamford Bridge 10 months ago after being ousted following Roman Abramovich's takeover.
He recently made an attempt to take control at Sheffield Wednesday but his offers of investment were turned away.