The former Republic of Ireland defender had a loan spell with Aberdeen in the second half of last season, and Calderwood hopes he can be persuaded to stay.
Maybury, 29, had admitted he would "prefer" a move to an English club, however he has not ruled out signing permanent terms with Aberdeen.
He is a free agent, having been released by Leicester, and among a group of five players Calderwood is keen to recruit in the coming three weeks.
"At the moment we are working on taking in another four players plus Alan," Calderwood told the Evening Express.
"We are aware of the interest being shown in him from England but hope he will eventually choose to stay with us.
"Alan has promised to let us know within the next four days or so. If it's bad news we have alternatives, but we won't look at those until we've had the final word from Alan."
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