The offer was described as "wholly inappropriate" by the board at the Close Brothers.
City AM had reported that the bid would be above $1.5 per share and conditional on due diligence.
Close Brothers has a market cap of $2.3 billion compared to Cenkos' $272.8 million, illustrating just how audacious the bid was.
Mr Stewart, a horse racing fanatic, has a reputation within the City and the rumours will only add to his persona. Close is suffering from a slowdown in its high-risk market-making business and its market value has dropped.
Founded in 1878, Close would have represented a massive coup for Cenkos with City AM describing the bid as a "David against Goliath takeover".
But the Close Brothers re-buffed the approach saying: "The board does not propose to pursue discussions with the consortium."