Roberts was the player offered as a makeweight in the failed Riyad Mahrez bid by City during the January transfer window, but Foxes manager Claude Puel still holds an interest in the 21-year-old currently on loan at Celtic.
Hammers boss David Moyes was also keen on signing the England Under-20 international last month and it is believed Pep Guardiola will allow the attacker to leave the Etihad Stadium at the right price.
£15m too much?
The proposed Mahrez deal collapsed because of the difference between how much Leicester and the Citizens valued the Algerian.
The Leicester Mercury reported that £50m plus Roberts was offered, so with the youngster being valued at £15m it took the overall value of the transfer to £65m.
Yet the 2015/16 Premier League champions disagreed with this valuation of the Englishman, instead asking for £80m and no player for Mahrez and, as a result, nothing was completed.
If the Foxes did not think Roberts was worth £15m then, does that mean if West Ham offer the same amount in the summer they should win the race for the current Hoops loanee?