The Daily Mirror say West Ham have placed a £60m valuation on Marko Arnautovic amid interest from Manchester United.
United boss Jose Mourinho saw the forward play for Austria against Russia last week, sparking reports that he wants to sign him.
Arnautovic briefly played under Mourinho at Inter Milan and has been touted for a summer move after impressing last season.
West Ham are in talks to sign Yaya Toure on a free transfer now his Manchester City contract is expiring, the Daily Mail reports.
And the Mirror say West Ham have joined City and Napoli in a battle to sign Southampton midfielder Mario Lemina.
Meanwhile, Tottenham will make Aston Villa an offer for Jack Grealish, according to the Daily Telegraph.
Villa have suggested they will not sell Grealish, reportedly valued at £40m, on the cheap despite their financial problems.
But the Telegraph say those problems mean Spurs chairman Daniel Levy will believe he can get the midfielder for as little as £15m.
The newspaper say Grealish would find the chance to move to the Premier League and play under Spurs boss Mauricio Pochettino appealing.