The Serie A outfit see the successful Dutchman as a suitable candidate to replace Edy Reja at the helm of the Stadio Olimpico but remain linked to Zola and Gasperini
The 66-year-old Reja announced after Lazio's last match of the 2011-12 campaign that he would leave the club this summer, and the Stadio Olimpico side are keen to find his successor sooner rather than later.
The Biancocelesti have been linked with coaches such as Gianfranco Zola and Gianpiero Gasperini, but they have now reportedly set their sights on Van Gaal.
The successful Dutch trainer has been out of work ever since he left Bayern Munich towards the end of the 2010-11 season.
Van Gaal was set to become Ajax's new sporting director earlier this year, but his appointment was eventually vetoed by a local court following a boardroom dispute at the Amsterdam giants.
The 60-year-old is also being linked with the position of sporting director at Liverpool.