Iwobi, 21, became a regular first-team player for Arsenal last season and was rewarded for his talents with a new long-term contract in April.
However, he has failed to hit the ground running this season after making one Premier League appearance so far this term.
He started on the bench for Arsenal in their 4-3 win over Leicester, but failed to get on the pitch.
And he had an 11-minute cameo in the 1-0 defeat to Stoke last weekend.
The Nigeria international could feature in the Premier League clash against Liverpool tomorrow (4:00pm).
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But he likely to start on the bench once again with Alexis Sanchez set to make his much anticipated return from injury.
However, Turkish outlet Takvim claim he could be set for a shock move away from the Emirates this summer.
It is said Galatasaray are interested in taking him on loan for the season.
This is something Arsene Wenger could welcome as his development could be boosted by starting on a regular basis.
The report adds Galatasaray sporting director Cenk Ergun could fly to London next week for talks with the Gunners to try and get a deal over the line.
Iwobi is contracted to Arsenal until the summer of 2020.