West Ham have made a £13m offer for Chelsea defender Emerson and proposed a £10m bid for Bruges captain Hans Vanaken.
Emerson has offers from Nottingham Forest and Atalanta while Juventus have been monitoring developments, highlighting that the 28-year-old is not short of options.
Meanwhile, manager David Moyes is hopeful the club can conclude a deal for Paris St Germain centre-back Thilo Kehrer this week if they can overcome some financial details.
However, a deal for goalscoring midfielder Vanaken will prove difficult with Bruges wanting to keep their captain.