The ambitious Dubai-based club, who named Diego Maradona as their new coach earlier this month, had an initial bid turned down by Atletico but believe they can secure Forlan on a one-year loan deal.
"After rejecting Al Wasl's initial bid for Diego Forlan, Atletico Madrid are now considering a new offer," a statement from Al Wasl read.
"A new and improved bid has been submitted for Diego Forlan - the new offer of taking Forlan on a year-long loan starting next season will be the final attempt by Al Wasl.
"Forlan has expressed his desire to join Al Wasl and is impressed by the club's vision and forward thinking strategy especially after appointing Maradona as coach - the Uruguayan international has recently declared his intentions of exiting the Spanish club.
"Forlan was expected to visit Dubai this week to negotiate personal terms with Al Wasl, but the club has confirmed that Forlan's visit has been postponed while they wait on Atletico's reply."
Forlan won the Golden Ball at the World Cup finals in South Africa after his five goals helped Uruguay to the semi-finals.
The 32-year-old struggled for form with Atletico this season, however, managing just 10 goals in all competitions to prompt speculation about a move away from the Spanish capital.