Sean Dyche saw his side get off to a spectacular start this season, beating Premier League champions Chelsea 3-2 on Saturday, and Sky Sports report that the manager is ready to bolster his attack in the wake of Andre Gray's departure.
Gray joined Watford on a five-year deal - believed to be worth £18m - earlier this month after rejecting a new deal from his former club.
The Clarets are keen on replacing their departed attacker, and have already seen two bids rejected by Leeds United for Chris Wood. The New Zealand hit-man registered 30 goals for the Championship side last season, and was also their Player of the Year.
Andone, meanwhile, notched 12 goals in 37 appearances for Deportivo last season. The 24-year-old garnered interest from Watford as well, while Fiorentina, Espanyol and Sporting CP are also thought to be monitoring.
Dyche is obviously sore over losing Gray, but he says he won't be crying over it.
"There's still a level this club operates to," he said last week. "It makes it tough at times, but it's the reality. I'm not going to start crying it in but it is difficult.
"No-one wants to lose their best players, but there's a reality to all clubs, particularly this one. Andre had a year left on the contract and it's normal football business. We went as far as we could (with a contract offer)."