Lacazette, 26, looks set to leave Lyon in the coming months.
The prolific striker was being heavily linked with a move to Atletico Madrid.
However the Spanish giants won't be able to sign anyone until January after a FIFA-imposed transfer ban was upheld last week.
And, according to TMW, that has increased the chances of Lacazette joining a Premier League club this summer.
They claim Arsenal, Liverpool and United are all interested in signing the France international.
The Gunners will be unable to offer the forward Champions League football having missed out on a top four spot for the first time in 20 years.
Jurgen Klopp and Jose Mourinho meanwhile, are both preparing for a return to Europe's elite club competition.
Lacazette, who TMW claim Lyon value at around £44m, scored an impressive 37 goals in 45 appearances across all competitions this season.
There are still two years left to run on his current deal.
But he has already announced his intention to seek pastures new this summer, saying: "I think that's [this summer] the right time.
"I want to discover something else, and to play at a different level.
"I know very well that on a European scale I am not yet well recognised.
"I want to see if I can answer the questions that people are asking, and to make further progress."
