New Middlesbrough manager Strachan was regularly linked with the centre-forward while in charge at Celtic - but had been unable to get close to the £5m asking price.
Watford-born Mackail-Smith, 25, has now emerged as Boro's top target after making an impressive start to the season at London Road.
A source said: "Gordon's admiration of the player is well known and he is certain to make a move for Mackail-Smith in the January window."
Former Leeds and Manchester United midfielder Strachan took over at Boro last week after Gareth Southgate was axed.
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