It comes after the airport said service levels were "excellent" over the bank holiday weekend (7 April) despite industrial action by members of the union.
"We have listened to colleagues on the pay offer and have proposed changes they have asked for," an airport spokesperson said.
"This is a materially different proposal, which we believe Unite should let their members have a say on."
More than 6.2m passengers flew through Heathrow in March, a million more than in February, and 31 March was one of its busiest days since 2019 with 221,606 passengers.
