BBC Sport understands that the 28-year-old DR Congo international will hold discussions with Brentford director of football Phil Giles in the coming days, with multiple Premier League clubs actively pursuing a deal.
Newcastle United, Tottenham Hotspur and Nottingham Forest have all expressed strong interest in Wissa, who is believed to be open to a move - particularly with European football on offer from all three sides next season. Sources suggest that personal terms would not be a stumbling block, particularly with Tottenham and Newcastle, whose interest has ramped up in recent days.
Wissa is said to be unsettled by the recent transfer speculation and is weighing his options. While he is expected to rejoin the squad once they return from Portugal, that could change depending on the outcome of talks with club officials.
Brentford are understood to have made attempts to open negotiations over a contract extension, but Wissa - who turns 29 in September - is thought to be leaning toward a move away from the Gtech Community Stadium.
His potential exit would mark a second significant departure for the Bees, following Bryan Mbeumo's 65 million pounds move to Manchester United earlier in the window. Brentford had originally hoped to keep at least one of the attacking duo, but the growing likelihood of Wissa's departure is forcing a reassessment of their transfer strategy.
Wissa has just 12 months remaining on his current contract, although Brentford do hold an option to extend for a further year. The club may consider cashing in now to avoid losing a valuable asset for a reduced fee later - with a valuation around 40 million pounds being discussed.
Since arriving from French side Lorient in August 2021, Wissa has made 149 appearances for Brentford, scoring 49 goals in all competitions. He enjoyed his most prolific Premier League campaign last season, netting 19 times in 35 appearances.
Brentford will play their first pre-season friendly against Gil Vicente at the Estadio Cidade de Barcelos on 25 July, but Wissa's involvement - or absence - could speak volumes about where his future lies.
Marcus Rashford has completed a season-long loan move to Barcelona from Manchester United, marking a major development in the England forward's career following a turbulent period at Old Trafford.
Liverpool have completed the signing of French striker Hugo Ekitike from Eintracht Frankfurt in a deal worth up to 79 million pounds.
Brighton striker Evan Ferguson has joined Serie A giants AS Roma on a season-long loan deal, with the Italian club holding an option to make the move permanent for a fee in the region of 34.7 million pounds.
Bryan Mbeumo has completed a high-profile transfer to Manchester United from Brentford for an initial 65 million pounds, marking him as the Red Devils' third major signing of the summer.
