The 26-year-old was linked with a move to Old Trafford earlier this month, with club director Henrik Hoff revealing that the Red Devils had expressed an interest in the stopper as a potential replacement for Edwin van der Sar.
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"Manchester United have not been in contact with us directly, but I can confirm that there is an interest," Hoff told Ekstra Bladet.
"There is no smoke without fire. In case a big club like Manchester United show interest in our players, we are ready to negotiate."
However, United supremo Sir Alex Ferguson could now face competition for Lindegaard's signature from Parkhead boss Neil Lennon, who brought in his 10th player from a 10th different country on Wednesday following the arrival of Honduran defender Emilio Izaguirre.
Speaking to VG, Hoff confirmed that the Bhoys were keen to bag the custodian ahead of the Red Devils.
"It's no secret that Celtic are impressed with Anders," he said. "They saw him in our Europa League qualifier against Motherwell. In case an offer comes, we will discuss it."
Manchester United reserve team coach Ole Gunnar Solskjaer was also believed to have been present at Aalesunds' recent Europa League defeat to Motherwell.
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