Gylfi Sigurdsson of Swansea City is apparently Ronald Koeman's top priority, with Davy Klaassen of Ajax not far behind.
Everton have joined Liverpool and Arsenal in the pursuit of West Ham midfielder Manuel Lanzini, according to The Mirror.
"He was No. 10 at River Plate when he was 18 and that doesn't happen without a reason".
Lanzini was signed on a permanent deal for just £9.4million in March 2016 after impressing on an initial loan deal.
The former Argentinean U20 global has continued to impress this season having scored 8 goals in his 34 Premier League appearances so far to help Slaven Bilic's men maintain their top flight status for another year.
Defeat ended a hard first season at the former Olympic Stadium for West Ham, where fans are much further removed from the action than they were at the Hammers' compact former home at Upton Park.
Now rated at £8.50 million, Lanzini would represent a cheaper option than either Sigurdsson or Klaassen.
Andre Ayew hit the post from point-blank range twice in a matter of moments during West Ham's clash with Liverpool, a miss Graeme Souness described as one of the worst of the season.
Lanzini has been one of the few bright sparks in West Ham's season, becoming the club's talisman in the absence of Dimitri Payet who acrimoniously departed for Marseille in January.
And McAteer, who thinks West Ham's recent good performance will go all out of the window after their loss against the Merseyside giants, explained that he felt sorry for Bilic as the Croatian manager's future at the London Stadium will once again become a topic of discussion.