The negotiators were first seen in Barcelona by transfer experts, with the next sighting coming in Madrid.
There is speculation that United outcast Mason Greenwood is the subject of conversations with Spanish clubs.
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Greenwood is on loan at Getafe, where he has impressed by scoring six goals and providing five assists.
The Manchester Evening News, however, states that Murtough and Hargreaves were only in Barcelona for a routine meeting.
Murtough has been busy lately, as he has also met sporting directors at Juventus and AC Milan.