Gérard Houllier's position as Aston Villa manager is likely to become untenable if the club are knocked out of the FA Cup at Sheffield United and lose at Birmingham City on Sunday week. The Villa board have maintained Houllier's job is safe but, with supporters calling for the Frenchman to be sacked and discontent festering within the dressing room, Randy Lerner could be compelled to act if there is no immediate improvement in results.

Although the club's owner is desperate for Houllier to succeed after he appointed the 63-year-old as Martin O'Neill's replacement in September, the dismal run of form that has plunged the club into the relegation zone for the first time in seven years, together with the unrest that surfaced after Wednesday night's 1-0 home defeat by Sunderland, when Villa fans chanted "You're getting sacked in the morning", has placed Lerner in a difficult position.

Lerner has worked hard to rebuild bridges with fans disenchanted under the previous regime but the Villa owner risks damaging that relationship if he shows blind faith in Houllier. Sacking Houllier would be an admission that Villa made a mistake in appointing him in the first place but accepting that error – as Tottenham Hotspur did with Juande Ramos in 2008 – would be a small price to pay compared with the financial catastrophe of relegation to the Championship.

Villa made a record loss in their last set of accounts, which showed their wage bill had climbed to £71m – £11m higher than Tottenham's – and the figures for the 2009-10 season are expected to be every bit as bad. Life outside the Premier League would deepen the pain. There is a bonus system in place for the players if they qualify for the Champions League but there is no provision in contracts for salaries to be cut in the event of relegation.

The knee-jerk response to talk of Villa dropping into the Championship is that the club have far too many good players to go down. Yet that argument ignores the relegation form Villa have shown since Houllier took over – 14 points from 16 matches and only three league victories – and the growing disenchantment within a dressing room where the Frenchman's methods and approach to the job are a source of bemusement and frustration to many of the senior players.

Wednesday night was a case in point. Having produced a sub-standard performance against Sunderland, which culminated in Villa's sixth defeat in eight league matches, the players were amazed when Houllier elected to praise rather than scold them. It is understood that on another occasion the Villa manager said next to nothing when he came into the dressing room at half-time, effectively leaving the players to conduct the team-talk themselves.

Arguments with players have also been a feature of Houllier's reign, and Stilian Petrov, Villa's captain, placed the manager in an awkward position after the Sunderland game when he called on him to end his feud with John Carew. "I think the manager and [John] need to sort that out between themselves," Petrov said. "They are grown men and I think everything is about the club. If you want to have someone in the team you need to go and see what he can do. John has been a big figure here and we have missed him."

Sources close to Carew say it is unlikely he will play for Houllier again and that he has made up his mind he wants to leave Villa. The Norwegian fell out with Houllier at Lyon and before the Frenchman was appointed at Villa Carew ranked him bottom in a list of the seven managers he had played under. Houllier has at least managed to reintegrate Richard Dunne into his plans after a training ground row but Paul Faulkner, Villa's chief executive, is believed to have played a key part in their rapprochement.

Getting the Villa supporters back on side promises to be much more difficult. The reality is that the fans did not take to Houllier when he was unveiled and the combination of poor results and his bizarre behaviour at Anfield deepened their suspicion that he is not the right man for the job. It remains to be seen whether the FA Cup will provide some respite. "Where we are at the moment I will take staying in the Premier League," Petrov added. "I won't even care about the Cup. I am sorry to say that."