Arnautovic has been linked with a move to Chinese club Shanghai SIPG, with British media reporting that West Ham had rejected a £35 million (A$63 million) bid from the Chinese Super League champions.
The 29-year-old is West Ham's joint top scorer this season with eight goals in all competitions and Pellegrini said that although he had final say on the potential transfer, he had not asked the owners to reject offers for Arnautovic.
"If I say the player must stay, the player will stay," the manager told reporters. "I don't have any problem with the club. "They are not forcing me to sell Marko Arnautovic.
"In all the months I've been working here I never had any problems with the owners about that."
Pellegrini, who spent two years managing Chinese club Hebei China Fortune, said he understood Arnautovic's desire to move to China due to the high wages on offer.
West Ham, who beat London rival Arsenal last weekend to climb to ninth in the table, visit Bournemouth in the Premier League on Sunday.
