The Red Devils have been linked with a surprise move to sign the Austria international in the 2018 summer transfer window.
Manchester United boss Jose Mourinho was spotted at Austria’s 1-0 win against Russia in their friendly last week.
Arnautovic worked with Mourinho for a brief spell at Serie A giants Inter Milan before the playmaker moved to the Bundesliga.
The 29-year-old moved to West Ham in a £25m deal from Stoke City in the summer transfer window following five seasons at the Britannia Stadium.
Arnautovic scored 11 goals and made six assists in 31 games during his first season at the east London outfit.
However, former Newcastle and West Ham goalkeeper Hislop doubts that Arnautovic’s proposed move to Manchester United will happen.
“Who would leave West Ham for Man United?,” Hislop told ESPN FC.
“Who would leave Pellegrini for Jose Mourinho? Nobody, nobody.
“In all seriousness, I like Arnautovic a lot, but I just don’t see him going to Manchester United.
“He’s playing a big part at West Ham, I just see him as a bit-part player if he goes to Old Trafford.
“It doesn’t make sense to me.”
The Red Devils haven’t won the Premier League title since 2013 when Manchester United won their final top-flight crown under Sir Alex Ferguson.
Manchester United lost 2-1 to La Liga giants Sevilla in the Champions League round of 16 to make a premature exit.
The Red Devils lost 1-0 to Chelsea FC in the FA Cup final at Wembley last month.
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