Fernandes's interest came as a shock to Allardyce, who was axed after changes in ownership at both Newcastle - when he was fired six months into owner Mike Ashley's tenure - and Blackburn, where the same thing happened 24 days after a takeover by Venky's.
"I'm bemused," said the new West Ham manager.
"My information is that David Sullivan was not wanting to sell because it's his club, the club he's always supported.
"That was one of the reasons I took the job, because I didn't want any factions in terms of change of ownership because my reputation has already suffered by new ownerships at Newcastle and Blackburn dispensing of my services when there was no real credibility in it. It wasn't down to how I performed."