The Premier League says Manchester City have not broken any rules regarding Frank Lampard’s contract extension and that there is no agreement in place between the club or its owners and New York City FC over his registration.

The midfielder was expected to join the MLS side this month following what City originally described as a short “loan” period at the Etihad for the first five months of the Premier League campaign.

The 36-year-old has since decided to stay in England, leading to confusion over which club actually owns his contract and his future registration. Neither City nor NYCFC have responded to detailed questions from the Guardian over the nature of the deal. However, the league is satisfied that City have not breached any rules.

A league statement said: “Frank Lampard is registered as a Manchester City player until the end of the 2014-15 season. The Premier League has sought and received assurances from Manchester City that there is no agreement in place between the club or City Football Group with New York City FC relating to the player.”

Having left Chelsea at the end of last season, in July, New York City were clear that they had signed Lampard, declaring on their website: “New York City FC signs Frank Lampard to a Designated Player contract … a two-year contract which starts August 1st.”

Only a month later City said Lampard would arrive “on loan” – although that online announcement has since been removed despite Lampard referencing “loan” in media interviews.

MLS now says that Lampard was in fact signed last July by City Football Group [CFG], the umbrella company owned by Sheikh Mansour which runs City as well as clubs in Melbourne and New York, to play in MLS in 2015 and 2016. The intention was always for Lampard to join City until the end of 2014 before moving to New York, although he was expected back by the start of 2015.

However, on New Year’s Eve, City announced that Lampard’s “contract” had then been extended, while the manager Manuel Pellegrini has suggested that Lampard could even stay longer.

Although Lampard has another year left on his contract with CFG, he is yet to reveal what he intends to do in the summer – move to New York or stay at City for another season.