Everton have had a £30m bid for Arsenal winger Alex Iwobi and a loan offer for Manchester United defender Chris Smalling rejected.
The Toffees are expected to return with an improved bid for 23-year-old Nigeria international Iwobi - but it is likely to have to exceed £40m to be accepted.
Iwobi is not agitating to leave but is willing to move if a deal is agreed.
Smalling, 29, is one of seven centre-backs at United after the £80m signing of his England team-mate Harry Maguire.
He has made 323 appearances for the Old Trafford club, winning Premier League titles in 2011 and 2013.
Meanwhile, Everton are still pursuing Crystal Palace winger Wilfried Zaha.
In July, the Toffees confirmed an initial bid for the 26-year-old Ivory Coast international had been rejected, but denied making a second players-plus-cash offer.