Marko Arnautovic is set to miss West Ham's match against Bournemouth on Saturday after his proposed move to China 'collapsed'.
The Hammers had already rejected a £35m bid from Shanghai SIPG, but were anticipating a follow-up offer. Arnautovic was known to be keen on the move, which would have earned him £200,000 a week.
Pellegrini said at his pre-match press conference on Thursday that West Ham's owners had left the decision over Arnautovic's future in his hands.
"Absolutely, 100 per cent sure. I have the final say. If I say the player must stay, the player will stay," said Pellegrini, quoted by the Mirror.
"I don’t have any problem with the club. In all the months I’ve been working here, I never had any problems with the owners about that. So they are not forcing me to sell Marko Arnautovic.
"But I think, as a manager, the best thing is to take the solution that is best for the player and the club. Both together. If they agree, we don’t have any problem to change."
Arnautovic joined West Ham from Stoke in 2017 and was named 'Hammer of the Year' after scoring 11 goals in his debut season. He has added another seven to his personal tally this season.
Important though Arnautovic is, West Ham won three out of four matches when he was out injured last month, so there is evidence that they can survive and thrive without him.