The 25-year-old bumped into the Three Lions boss in a coffee shop in London following his side's League Cup triumph over Bradford, in which he scored a brace.
Dyer told The Mirror: "He was right there sat next to me, by coincidence. He said, 'Congratulations, well done'. I haven't seen him since, but I would love to pull on an England shirt.
"It is a massive achievement to represent your country. I am working hard for my club and trying to perform to the highest level. If it ever does come, I would never say no.
"It would be good to get back to Wembley sooner rather than later."
Swansea play Arsenal at the Liberty Stadium on Saturday.