Liverpool manager Brendan Rodgers confident that 'genius' psychiatrist Steve Peters will keep working with Premier League leaders

For a man who evidently took some convincing that moving into the unreconstructed world of football was worth his while, Dr Steve Peters is getting into the warp and weft of Liverpool. Having initially worked with them only one day a week, he was in a club suit with the team for last Sunday's critical win at West Ham United.

Other clubs are looking on enviously at the belief Peters has clearly inculcated, with Ronnie O'Sullivan, who was revived by the psychiatrist to win a fourth world snooker title, tweeting: "Best signing Man Utd can make is Steve Peters. They will win the league again. Got no doubt."

Ahead of the most important league game at Anfield in 24 years, against Manchester City on Sunday, Liverpool's manager, Brendan Rodgers, deftly indicated that Peters would be working for him, rather than rebuilding the fabric of a psychologically frayed United. "He's had chances to go to other clubs but he is very, very happy here, so it's a very important component in our team, in order to help us win," Rodgers said.

Interest from other clubs in the man who will also help Roy Hodgson's England players in Brazil this summer is not surprising, given that the prime quality about this Liverpool team is their self-belief and a capacity, so far, to remain calm under the immense expectation which habitually resides around the Anfield Road.

The 4-0 win over Tottenham Hotspur 12 days ago, amid what Rodgers described as "background noise" about whether his players would bottle it, revealed most about their grace under pressure. "Fearlessness" is a word Rodgers – and coincidentally Everton's Robert Martinez – uses to describe the mentality he is trying to create. "There's certainly no fear because as coaches and managers that's what we work for – for players to be fearless," he said.

Rodgers must take credit for the Peters effect. Other managers are unwilling to let outsiders take on part of the management role. Football's insularity, in that respect, was evident last year when Roberto Mancini, then Manchester City manager, met UK Cycling's performance director Sir Dave Brailsford, under whom Peters worked so effectively. Mancini turned up late and the press conference entailed Brailsford discussing what football could teach him. There was little sense that knowledge might flow football's way.

This would probably not have surprised Peters. "When I met Steve he was not sure about football because he'd been kept at arm's length and the experiences he had in it briefly were not very good," Rodgers revealed. "He realises he's got someone [in me] who knows about psychology and the confidence players require to perform and the mental skills involved, which doesn't happen much in football. [As a manager] you know 90 per cent. You can't know everything. It's very important you have the team around you to fill those gaps."

Peters, who asked Rodgers for permission to work with Hodgson, will be telling Liverpool's players this weekend what he reminded them of at Upton Park and what he told The Independent last year in an interview which seems more prescient than ever as Liverpool have a title within their grasp. The message is still to make the title a dream rather than a concrete aim because football – like any sport – involves an opponent whose performance level is something Liverpool cannot control.

Rodgers employs his own psychological strategies. He carves the season up into five-game blocks, for instance, and the West Ham game was the start of a new block. To the question of whether Peters was his most crucial signing, he replied: "No. He's not a magician." And he will not be seeking to increase the psychologist's involvement beyond the one-to-one sessions Peters provides for players who seek him out.

"He just works with individuals, there's no change and no need to," Rodgers said. "It's about reinforcing things. [Steve] is a specialist in what he does and a genius in that field. He's also great for me because command can be lonely. You're trying to put in place a structure and environment that's dynamic and forward-thinking, and he's also good for me to bounce ideas off. He's got many experiences, not just in sport, but also in life, so he's a very important part of the team. But I don't want to say he's the best signing. They're all good signings."