Parkinson could see off a reported Sunderland job rival.
Sunderland could go head-to-head with a manager with whom they reportedly made contact after Jack Ross's sacking for a January striker target.
And Parkinson is said to be willing to pay £250,000 to land him.
Boyce has scored 13 goals in 31 games for Burton this season, but with his contract due to expire at the end of the campaign, it is claimed that Nigel Clough may have to sell.
Boyce is top of Stendel's Hearts wishlist, according to The Sun.
But it remains to be seen whether the Scottish side can compete with Sunderland financially.
The Sunderland strikers Marc McNulty (to Hearts' city rivals Hibernian) and Will Grigg (Blackpool) have each been linked with moves away from the Stadium of Light this month.
And the arrival of Boyce - a 21-cap Northern Ireland international - could accelerate their departures.
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