But he has been told that one or the other – probably Snodgrass – will have to be sold as the Irons continue look to plough further funds into the squad building programme.
Amid strong speculation that Arnautovic could be on his way to us within the next 48 hours, a decision will have to made on the two current wingers.
Arnautovic is a big priority for Bilic but to bring him in one of the other two will need to be sacrificed despite manager liking them both and even holding private talks with them explaining they are very much part of his thinking this season.
However, it would be a big shock if both were to remain with the Hammers considering a second striker – to hopefully join Javier Hernandez – remaining on the cards.