Clarets boss Vincent Kompany wants to add a new goalkeeper to the ranks ahead of a season of Premier League football.
Kompany is keen to raid his former club Anderlecht for Verbruggen and Burnley are backing their manager.
The Turf Moor outfit have put in an offer of £13m to sign the shot-stopper and believe they can convince him of the merits of the move if they can agree a fee.
Verbruggen is also of interest to Liverpool and Manchester United.
However, it is claimed he is not keen on joining either of the two Premier League powerhouses as he would not start games immediately.
Burnley have that in their favour and the goalkeeper may be drawn towards the idea of week in, week out Premier League football under ex-Anderlecht boss Kompany.
Verbruggen is just 20 years old and came through the youth ranks at Dutch side NAC Breda.
Anderlecht snapped him up in 2020 and he won the club’s Player of the Season award this term.
