Gazzetta dello Sport says Twente want £2 million from Inter immediately to fund their own transfer plans, with the remainder of the fee - around £8 million - due in January.
But Arnautovic's foot injury has Inter concerned and they do not want to commit to anything until the Austrian's long-term fitness is assured.
Meanwhile, want-away Bayern Munich defender Lucio is a new option for Inter.
Livorno midfielder Alessandro Diamanti is emerging as a top target for Inter president Massimo Moratti.
Moratti has confessed to friends he sees a lot of Alvaro Recoba in 26 year-old Diamanti.