Torres was an extra-time substitute during Spain's 1-0 victory over Netherlands in Johannesburg on Sunday, but ended the match in pain after pulling up sharply holding his groin.
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The 26-year-old striker has struggled with a succession of injuries since arriving at Anfield three years ago from Atletico Madrid.
He still managed to score 22 goals last season despite two bouts of knee surgery restricting him to just 32 appearances.
Torres is now back in Spain with the victorious national team and the Reds are preparing to send a medical team to Madrid to assess his latest injury scare.
However, Liverpool's new head of medicine and sports science, Dr Peter Brukner, is hopeful that the latest concern is not too serious.
"We've been in touch with the Spanish medical team and they don't think it's too serious. It's an adductor muscle injury but they've not had a chance to assess it today," he told Liverpool's official website.
"Fernando will have a proper assessment and probably a scan tomorrow and some of the Liverpool medical staff will go to Madrid later in the week to fully assess the injury and organise his rehab. At this stage we don't think it's too serious.
"We can't say too much more at the moment until it is properly assessed."