The Newcastle manager is eager to add cover for Fenerbahce-bound Emre Belozoglu, and is reported by the paper as having seen Inler perform at Euro 2008.
The 24-year-old has seemingly done enough to convince Keegan to pay Udiniese £4 million for his services.
Inler has spent only one season at Stadio Friuli, but wants to play in England's Premiership, according to the Mirror.
The midfielder had previously been at FC Zurich, and has won 15 caps for his national team.