Many Hammers fans are concerned that Arnautovic will seek a move to China, after a big money move was scuppered in January.
Arnautovic did not score between February and April, but he finally rediscovered his form in the last month of the season, scoring three goals in the final two games.
And Noble believes the Austrian is once again settled at the club.
"Have you seen a change in him? Well then obviously I have," said Noble to reporters.
"It is important [to keep Arnautovic this summer], of course. He is a top player and you can see that when he is back on his game. I am hoping, but I think he will be here with us next season.
"He is a top, top player when he is at it. Obviously he went through a bit of tough patch, but all in all he has been massive for us this season and I am pretty sure he will be again next season."