The Potters could be about to make a club-record offer for the Bayern Munich midfielder.
Liverpool have long been linked with a move for the Bayern Munich man but Stoke recently emerged as shock candidates.
And now boss Mark Hughes is said to be considering a club-record bid to trump Liverpool - as well as potential suitors Inter Milan.
The Telegraph also claim that Stoke have been in talks over Shaqiri for 'a few weeks,' although they are yet to have made a bid.
Stoke assistant boss Mark Bowen had earlier confirmed the Potters' interest in the Swiss midfielder:
"There are other clubs interested, but it doesn't mean we rule ourselves out. He's definitely on the list, but there is competition for a player of his ability.
"It's bound to help and it does help. There's many boxes to tick, not least the financial side of it, and with Shaqiri coming from one of the best clubs in the world, there's a lot of persuasion to get it done."