The Catalan giants were watching closely on Thursday when Lacazette scored twice against Valencia in the Europa League semi final.
The Gunners have named French international Lacazette as their Player of the Year after he netted 18 goals in all competitions this season.
Barcelona are keen to strengthen their squad this summer with another striker and have been impressed with his partnership with Pierre-Emerick Aubameyang.
Gunners boss Unai Emery knows that he has to offload players this summer to strengthen his squad but Lacazette is one of the players he is keen to hang onto.
But that is unlikely to put off Barcelona from trying for Lacazette who has netted 35 times in 85 appearances for Arsenal since becoming their £46.5m record signing in July 2017.
Barcelona have also been linked with Atletico Madrid forward Antoine Griezmann.
Lacazette is known to be close to Barca’s technical secretary Eric Abidal but no formal talks have been opened yet.
Arsenal boss Unai Emery has recently praised the French striker as well as Pierre-Emerick Aubameyang.
He said: “They are [helping] us with their performances, with their behaviour, with their commitment. We are happy together, sharing this way.”
And when asked if he prefers them playing together or just one as a lone striker Emery admitted he could be flexible.
He explained: “It depends. Sometimes they both play, sometimes one.
“It depends on each moment, on our tactical idea. Each match is different.”
Lacazette will look to impress again on Sunday when Arsenal take on Brighton at the Emirates in the Premier League from 4.30pm.
The Gunners are embroiled in a fight with Chelsea, Tottenham and Manchester United to finish in the top four.
And Emery’s side will look to capitalise on arch-rivals Spurs losing to Brighton on Saturday.
Arsenal could also qualify for the Champions League through winning the Europa League.