The 31-year-old Swiss star looked set for a move to the Foxes, where he had been identified as the ideal replacement for the departed Esteban Cambiasso by new manager Claudio Ranieri, according to a report in the Daily Mail.
The classy star's contract expires next summer and he has already turned down moves to Watford, Udinese and Besiktas this summer, according to Football Italia.
Inler would no doubt be able to call on the advice of international teammate Valon Behrami regarding a move to east London, as the Watford midfielder was a Hammers fans' favourite during his time at the club.
He would have arguably made the ideal replacement for Cambiasso at Leicester, with the Argentine another player who had been linked with a move to West Ham, as reported by the Daily Mail.
According to the latest reports, though, east London is a more likely destination for Inler, which would surely end any interest in bringing Leicester's player of the season, Cambiasso, to Upton Park.
Hammers In-ler for Gokhan but what does he bring?
But what would Inler bring to Slaven Bilic's side should West Ham seal his signature?
Well vast international experience for one. Inler, who has Turkish heritage, has made more than 80 appearances for Switzerland - scoring six goals - after electing to represent them over Turkey after playing for the U21 sides of both countries as a youngster.
His former clubs include Basel and Udinese, before completing a big move to Napoli where he was the midfield playmaker in the Andrea Pirlo mould. He helped both Italian sides into the Champions League.
Is he a potential replacement for Song?
Inler has an eye for the odd spectacular goal and has played at the European Championships and two World Cups with the Swiss national side, captaining them to the last 16 in Brazil last summer.
A move for Inler may be forced through amid continuing doubts over a deal for the injured Barcelona star Alex Song, who was on loan at West Ham last season.
They are similar players, although Inler would perhaps be a shorter term signing given his age and West Ham's new transfer policy aimed at predominantly signing players no older than 27.