Manchester City have denied making a second bid to Napoli to sign midfielder Jorginho.
Sky in Italy are reporting that City have made a fresh offer of £41.2m + between £4.4m and £5.3m in add-ons.
Napoli president Aurelio De Laurentiis said on Sunday that they had rejected a bid just shy of £44m (£39.5m + £4.4m add-on) from City for the player.
Talks remain ongoing as the two clubs try to find a way to complete the deal, after Sky in Italy reported the two clubs were in advanced negotiations last week.
Sky in Italy are reporting that City are unwilling to wait more than a week for a response to their latest offer, and they may already have an alternative target ready should the deal fall through.
Sky Sports News reported in April that City had identified the 26-year-old Italy international, who was born in Brazil, as one of their primary transfer targets for this summer.
He scored four goals in 39 appearances last season, and has scored six goals in 160 games for Napoli since signing from Verona in 2013.