Tottenham and Chelsea faced off at Wembley in last season's Capital One Cup final
And Spurs could even be playing their Champions League games at Wembley next season, having already secured qualification for the competition this year.
Chelsea are also in talks to use Wembley, Dyke revealed, but their stay would more than likely be a three year deal, while they redevelop their Stamford Bridge home.
Spurs have already begun constructing a new £400m, 61,000 capacity stadium next door to their current White Hart Lane home, and it is scheduled to be ready for the 2018-19 season.
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Dyke confirmed that a season-long deal with Spurs is close - and that Champions League games could be played at the national stadium next season with the capacity at White Hart Lane reduced because of construction work.
The FA chairman said: "'We are certainly in discussion with Spurs that they should come in for the full season when they're rebuilding their stadium.
"I think we're a long way down the path on reaching an agreement."