The 22-year-old featured against Shrewsbury in a reserves friendly on Tuesday which the Shakers won 1-0.
Ainsley is out of contract at Portman Road in the summer but will be allowed to leave in the January transfer window if he can find a new club.
The former England Under-17 international has made just one league start for the Tractor Boys this season along with two substitute appearances in the Capital One Cup.
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