Another way to go might be that Chekov is still aboard the Enterprise, and is referred to as being so (down in engineering?), but while we hear of Chekov, we never see him.
While feasible, I think it'll feel a bit of a downgrade regarding his role from part of Kirk's inner circle to down somewhere in engineering that they decided to mention once in a while. I mean yes, he had a stint replacing Scotty but even then Into Darkness gave him a bit of an onscreen presence because he's an important member of the crew. Just mentioning he's in the ship...Would raise some eyebrows.
It'll be like saying Spock and Bone are in the Enterprise B in the start of Generations...But they got lost walking around the cargo area the entire trip.