The Daily Star says Rashford's arrangement includes a permanent option set at €40m.
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And the Catalans have already seen enough to explore triggering the clause, though not at the current price.
Barca are pushing United to lower their price to €30m with management now eager to keep hold of the England international.
Rashford has already made six appearances and scored his first goals with a double in last week's Champions League victory over Newcastle.
Rashford's deal with United runs to 2028.
