Construction union UCATT's general secretary, George Brumwell, said he was hoping to sign a deal with Multiplex in the next two weeks.
He said: "We are looking to get the kind of terms and conditions in place that have been agreed on the Terminal 5 project."
Laing O'Rourke is to pay its skilled workers £55,000 a year at Heathrow.
Brumwell said he wanted adequate terms and conditions agreed at Wembley before a pay deal was finalised but he refused to give details.
Negotiations are also under way at Wembley between Multiplex and M&E union Amicus.
Using conditions set out in the major projects agreements for M&E contractors, signed last month, Amicus is calling for electricians' salaries to be set at more than £50,000 a year. Under the claim, electricians would earn a minimum of £13.32 an hour in return for improved performance and good industrial relations.
Harry Cowap, an Amicus official, said he was liaising with Multiplex on a daily basis. "We do not want workers on Wembley to be restricted in their earnings," he said. "I will negotiate locally to secure bonus payments if required."
Multiplex said it would "work closely and proactively with the unions".