He played nine times, scoring once, in season 2020/21 before returning to the Blue Toon last term.
He featured 15 times as Peterhead finished seventh and has impressed McInally enough to offer a permanent move to the north-east club.
However, the former Dundee and Dundee United man admits he’ll have to be patient as Strachan weighs up his options.
McInally told the club website: “We have made Danny an offer which he is considering, but he wants to pursue other offers so nothing is over the line.”
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