David Moyes says he would be interested in becoming West Ham manager, with the future of current boss Slaven Bilic set to be decided in the next 48 hours.
BBC Sport understands the Hammers have already held talks with ex-Everton and Manchester United manager Moyes.
Speaking to Bein Sports, the Scot denied there had been contact, but said he wanted to return to club management.
West Ham are one point above the Premier League relegation zone after Saturday's 4-1 defeat by Liverpool.
Bilic acknowledged after the game that he was under "big pressure" and in a "very difficult" situation.
Moyes said: "I've always said I want to go back into club management. If the right opportunity comes around, I'll be interested."
Asked about West Ham, the 54-year-old said: "I am interested but at the moment that vacancy has not become available. I know what Slaven must be going through."
Moyes' former assistant at Everton Alan Irvine could be a candidate to join the Scot's coaching team at West Ham should he be appointed.
Bilic's position was discussed in October, but the club's owners opted to give him more time to improve results.
Despite victory over Tottenham in the EFL Cup a few days later, the Hammers drew their next Premier League match against Crystal Palace and were then thrashed by Liverpool.
Bilic's side have won just two Premier League matches this season and have lost three of their past four games at London Stadium.
Former Hammers manager Sam Allardyce told Match of the Day on Saturday that it "wouldn't surprise him" if Bilic was sacked.
Bilic, 49, replaced Allardyce in June 2015, and led the side to seventh place in his first season in charge.
But an 11th-placed finish last term, their first at London Stadium, has been followed by a poor start this season.
Moyes' most recent managerial job was at Sunderland - he resigned after they were relegated to the Championship in May.
West Ham's next match is at Watford on Sunday, 19 November.
Phil Neville, speaking on Radio 5 live
I hope David Moyes gets the opportunity to get the job. I watched the West Ham game yesterday and Slaven Bilic is under massive pressure, he looks like someone when he's stood on the touchline who probably needs relieving of the pressure.
West Ham look like they need a change and I think David Moyes is perfect. He's had a couple of bad experiences but he's still a fantastic coach and I won't let anyone else tell me otherwise. He would do a fantastic job at West Ham.