But the Hornets reportedly face competition from Italian giants Lazio who are also said to be keen on the Colombian.
Borre, 25, is leaving Argentine side River Plate - where he played in the Copa Libertadores final in 2019 - and wants to come back to Europe.
His contract expires on June 30 and despite the Buenos Aires based side wanting to extend, the forward will leave El Monumental.
The Colombia international - who scored eight goals in 13 league appearances last season - was with Atletico Madrid early in his career before heading back to South America for more regular action.
Watford boss Xisco Munoz is looking for a couple of new strikers and Borre would fit in neatly with his limited budget.