Wyke left his hometown team without a senior appearance three years ago, but has gone on to impress in spells at Carlisle United and Bradford.
The 25-year-old has scored 20 goals in 48 games for the Bantams, after joining them for £250,000 a year ago.
And the Daily Mirror reports that his form there has alerted Middlesbrough, along with several other Championship sides.
It adds that Pulis, the new Boro boss, wants Wyke to improve his attacking options - with only Britt Assombalonga (12) and Martin Braithwaite (six) finding the net on more than three occasions this season.
The 6ft 1in target man will not come cheap, however, with Stuart McCall, the Bradford manager, telling Sky Sports this week that it would take £5 million to prise him away from Valley Parade.
As well as Assombalonga and Braithwaite, Middlesbrough have Patrick Bamford, Rudy Gestede and Ashley Fletcher to call upon up front.
Is Wyke better than Middlesbrough's current striking options?