Fey explained that Damon, who will appear in the season finale, approached her about a role in the sitcom.
"He came up to us at the SAG Awards," she told E! Online. "He came up to our table and was like, 'Hey, I want to be on your show'.
"And then Glee won Ensemble and he came up and he goes, 'No, I changed my mind, I want to be on that show'. And then he came back a third time and was like, 'No, I'm kidding, seriously, I want to be on your show'. So we were like, 'I think Matt wants to be on the show'."
Fey added that she believes Damon could reprise his role in the future, saying: "Hopefully he will [be back]. He lives here. He was like, 'I live here and my wife wants me to stay home', so hopefully he'll be back. When he's between movies we'll grab him, hopefully. We had a great time in the episode, so yeah, hopefully he'll be back."
The season finale of 30 Rock airs on Thursday at 9.30/8.30c on NBC in the US. The show continues on Monday at 10pm on Comedy Central in the UK.
> Fey hoping for Sheen '30 Rock' return