The festival founder said he has been in regular contact with Noel and Liam Gallagher of Oasis, adding that Swift would be well-adapted to the 'Dolly Parton slot', reported Digital Spy.
"I do talk to Noel and Liam a lot," said Eavis.
"Wouldn't it be marvellous for them to relaunch at Glastonbury, now Liam has split from Beady Eye?," he added
Oasis last headlined Glastonbury in 2004 along with Paul McCartney and Muse.
Swift has been rumoured as a potential performer at the festival following the news that she will be in the UK at the time as part of her '1989' world tour.
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