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But with Amorim reluctant to compromise his tactical philosophy, plus the cost of hiring him, any club that identifies the former Braga coach as their No.
But with Liverpool looking elsewhere, Barcelona persuading Xavi Hernández to U-turn on his decision to quit as coach and Bayern Munich closing in on Ralf Rangnick, the former Manchester United interim manager now coaching the Austria national team, the three big jobs Amorim had been linked with in recent weeks are all likely to be filled by somebody else.
West Ham might yet return for more detailed talks than last week's flying visit if, or more likely when, they part company with David Moyes.
If either Chelsea or Manchester United create their own managerial vacancy this summer due to ongoing doubts over the future of Mauricio Pochettino and Erik Ten Hag respectively, Amorim could yet land the big job that his track record at Sporting is pointing toward.
Up front, the prolific Sweden forward Viktor Gyökeres, a bargain €20m signing from Coventry City last summer, has scored 26 goals in 30 league games this season, including two in 60 seconds against Porto on Sunday to salvage a point in a 2-2 draw.
Rúben Amorim deserves to be one of the most highly rated managers in Europe, but earning a job at one of the biggest clubs might be tough for him. Rita Franca/NurPhoto via Getty Images
However, it is the back three that is likely to make sporting directors at potential new employers nervous.
Louis van Gaal tried to make three at the back work at Manchester United and failed, while even Pep Guardiola has reverted to a four-man defence at Manchester City after trying out the system at times.
Overall, the cost of hiring Amorim -- in terms of compensation, wages and the potential outlay on suitable players -- would make him a difficult appointment for many clubs this summer.
The big clubs in the market for a new coach this summer lack either one or the other, or both, of those precious commodities to make Amorim the right fit.
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