The promising Spaniard has been in terrific goalscoring form during his season-long loan at Segunda Division side Real Zaragoza.
Borja, 22, has made just one senior appearance for Atletico since coming up through the ranks to earn his La Liga debut in 2010, having spent four consecutive season-long loans at Real Murcia, SD Huesca, Deportivo La Coruna and now Real Zaragoza.
The former Spain Under-19 international has been in prolific form for the second division side this term, however, scoring 20 goals in 32 games to attract interest from a host of teams.
La Liga clubs Villarreal and Celta Vigo are both tracking the 6ft 1in forward but Corriere dello Sport suggest that his future could lie outside of Spain, with a Premier League move a potential option.
Both Villa and Swansea have been named as interested parties and, with Atletico boasting the likes of Mario Mandzukic, Antoine Greizmann, Raul Jimenez, Fernando Torres and Angel Correa at their disposal, manager Diego Simeone is said to be open to a possible sale.
A switch to either team would make sense, with both needing reinforcements behind Christian Benteke and Bafetimbi Gomes, respectively, but what kind of fee his services would demand still remains unclear at this point.
The Madrid-native has less than 18 months left on his contract but, given his ongoing goalscoring success and past standing as one of Atletico’s top prospects, he still might not come cheap.
Borja isn’t the only Atletico striker linked to Villa in recent months either, with fellow front man Leo Baptistao, who is also on a season-long loan at Rayo Vallecano, another prime target for Tim Sherwood, per TMW.