The club recently sealed a Champions League spot after a remarkable Serie A campaign. Their strong season owed a lot to the finishing prowess of Ciro Immobile. The striker netted 36 times in the league and finished as the division's top scorer, five goals ahead of Cristiano Ronaldo.
But Lazio cannot rely on Immobile to carry the can all the time and may view Wood as a player who can add depth to their attack.
The 28-year-old bagged 14 goals in the recent Premier League season, his most in a single campaign, and reports suggest he is keen for a new challenge.
The New Zealand star has steadily progressed during his time at Turf Moor. He came as a proven Championship forward but needed to prove himself in England's top division.
Burnley will not want to lose Wood. He works hard for the team and battles for every percentage ball. It's not easy to be a striker for the Clarets but Wood has passed the character test.
However, the club shouldn't be fearful about a departure. If the reports are true and Wood is seeking a new challenge then bids should be welcomed. The club can manage that situation.
Filling the void
Jay Rodriguez and Ashley Barnes have proven themselves to be effective options for Dyche. The jury is still out with Matej Vydra but it's tough to fault the Czech's commitment to the team. At the very least, they are three players who understand what Dyche expects of them in the forward areas.
The hardest person to directly replace at Burnley is the manager. He is the football club. By comparison, the loss of any individual player is much easier to deal with. That statement could be challenged, of course, with the likes of Nick Pope and James Tarkowski. But the club have seamlessly coped with injuries to others in the past, including Wood.
Most recently, Ben Mee had been sidelined with a lengthy layoff and the Clarets simply carried on their unbeaten streak. Kevin Long slotted in as his replacement and the team adjusted seamlessly.
Dyche's very basic system is rarely too reliant on individual brilliance. The setup does most of the thinking for the player which means that it is an easy fit, for those of the right character and mentality, to slot in when needed.
Burnley would like to keep their record signing but it wouldn't be the end of the world if he moved on. The Clarets would no doubt expect to make a profit on their record signing.
Even with the world's recession, it's hard to imagine Mike Garlick accepting anything less than £20-million.
In short, Burnley hold the cards on this, if there is any truth to the reports.