Sky Sports News understands the Hammers have no intention of the selling the 29-year-old and value him at £50m.
Arnautovic joined West Ham from Stoke for a club-record £25m fee last summer and scored 11 goals during his debut season with the club.
The Austria international, who also contributed six assists during the 2017/18 campaign, has four years left to run on his contract at the London Stadium.
United manager Jose Mourinho was in the stands on Wednesday night as Austria claimed a 1-0 friendly win over Russia, with Arnautovic providing the assist for the winner.
Arnautovic previously worked with Mourinho during their time together at Inter Milan in 2009.
He made only three appearances for Inter during an unsuccessful loan spell at the San Siro from FC Twente and subsequently joined Werder Bremen in the summer of 2010.
Meanwhile, United remain in talks to sign Porto full-back Diogo Dalot and Shaktar Donetsk midfileder Fred as they look to strengthen their squad ahead of next season.
Sky sources understand West Ham are in talks to sign Genoa defender Armando Izzo and are also interested in Barcelona defender Marlon Santos with new manager Manuel Pellegrini aiming to sign up to five players this summer.
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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