The need for a centre-back was heightened on Saturday, when Emanuel Pogatetz was forced off seven minutes before the end of the win over Scunthorpe United with a hamstring problem.
Strachan fears the Austrian, who has already missed a large chunk of the season with knee trouble and a fractured cheekbone, will be out for at least a few weeks.
The injury situation, with Matthew Bates and Seb Hines also ruled out for the long term, has left Strachan intent on bringing in Caldwell at the early possible opportunity.
Celtic are willing to listen to offers for the 27-year-old, out of contract in the summer, but they are unlikely to receive the top price of £3m which they rate him at, with £500,000 a more likely figure.
But Boro could face competition from Caldwell's old club Newcastle.
Chris Hughton has him on his wanted list ... but there is no guarantee the Geordie boss will get funds in the January transfer window.