The north London club have long held an interest in Edouard and head coach Mikel Arteta is known to be an admirer of the 22-year-old forward, who scored 28 goals in all competitions for Celtic last season.
Juventus and Atletico Madrid have both made approaches to sign Lacazette in recent weeks and Arsenal have identified Edouard as one of their priority targets should their No.9 make his way towards the exit door this summer.
According to Duncan Castles, speaking on his Transfer Window podcast, Arsenal made an initial offer of £15 million which was turned down by Celtic.
He claims the Gunners have since increased their bid to £20m with add-ons up to the value of £2.5m which would be paid in instalments across a four-year period, as has been the case with Kieran Tierney and Nicolas Pepe.
Though the offer is just verbal, it could be formalised if Lacazette leaving becomes a real possibility.
It’s understood Lacazette is keen on joining either Juve or Atleti and Arsenal have responded by slapping a €40m (£37m) price tag on the France international.
At his press conference on Friday, Arteta played down speculation of an imminent move for Lacazette and insisted the attacker was ‘really happy’ to be an Arsenal player.
‘He is really happy here, he wants to keep improving and contributing to the team,’ the Spaniard said.
‘I know how good he is, the impact he is having.
‘He knows about the competition he has with the front players, and again he needs to demand of himself to be the best striker at this football club, the same as the rest.
‘Yes, I think he is very happy here. That is my feeling and what I got from that message.’