The 20-year old forward made 24 appearances last season and scored three goals in the FA Cup.
Newcastle see potential in the Denmark U21 international and have proposed £10million with a further £5m in add ons.
Negotiations are continuing with Osula keen to make the switch.
The Blades have been looking to bring in a replacement with Crystal Palace winger Jesurun Rak-Sayki among the names they have considered on loan.
William Osula has attracted interest from Newcastle United who are in talks to sign the striker
Sheffield United midfielder Ollie Arblaster is attracting Premier League interest from Everton, Leicester City and Ipswich Town among others.
The England U20 international impressed last season after a loan spell at Port Vale and could be available for around £12million.
Newcastle have already made three new signings this summer, bringing in Odysseas Vlachodimos from Nottingham Forest, Lloyd Kelly from Bournemouth, and John Ruddy on a free from Birmingham.
The Magpies also made Lewis Hall's loan signing permanent for £28m in July.