The Frenchman, who was named Arsenals Player of the Year earlier this week, has attracted Barcelonas attention as the Catalans seek a long-term replacement for Luis Suarez.
The La Liga giants had identified Marcus Rashford as a viable target but United are keen to extend his contract and prising him away from Old Trafford will cost in excess of £130million.
With that deal looking difficult, the Express claim Barcelona have switched their attention to Lacazette and were impressed by the double he scored against rivals Valencia on Thursday in the Europa League.
That took the Frenchmans tally to 18 goals for the season and Arsenal may struggle to hold onto him should they miss out on a Champions League slot.
Victory in the Europa League appears to be the Gunners best route back into Europes elite competition but, in any scenario, Lacazette may struggle to turn down Barcelona.
The striker is said to have a good relationship with Barcelona director Eric Abidal, though talks have not been opened just yet.