Barca filed a request to La Liga last week for permission to sign a new player after Dembele underwent surgery on a ruptured tendon in Finland, leaving him sidelined for six months. They are also without striker Luis Suarez for the next two to three months due to a knee problem.
La Liga maintains the right to authorise signings outside of the transfer window, which closed in January, on a case-by-case basis. The legislation states that if a player is ruled out for at least five months, a replacement can be signed.
The Catalan club sent La Liga the medical reports following Dembele's operation and, on Monday, they received notification that a panel of experts had confirmed the severity of his injury.
As a result, they have been given the go-ahead to make an emergency signing. However, they can only sign players already registered in Spain or that are without a club. They only have a 15-day window, too.
Sources told ESPN last week that Barca have looked into moves for several forwards already. Real Sociedad's Willian Jose and Real Betis' Loren Moron have been ruled out because of the money being demanded by their clubs.
Alaves' Lucas Perez and Getafe's Angel Rodriguez, who scored in his side's 2-1 loss at Camp Nou on Saturday, are seen as more affordable options, with sources explaining Barca only have around €12 million to spend.
However, the same sources say that none of those four are currently the leading target.
Sources at Barcelona would neither confirm nor deny interest in the Denmark international at this stage, while sources at Leganes said they had not yet received an approach from the Spanish champions for the player.
Coach Quique Setien has spoken of the need for a new signing in attack after being left with a small squad.
And following an injury to Jordi Alba at the weekend, Setien only has 15 fit first-team players to work with at the moment, including two goalkeepers, as preparations begin for upcoming games against Napoli and Real Madrid following this Saturday's match at home to Eibar.