Chelsea and Manchester City are due to meet in Istanbul on May 29 but Uefa’s plans for the all-English tie have been complicated after the UK put Turkey on its foreign-travel “red list”.
No English fans will be allowed to travel to the Ataturk Stadium in Istanbul and talks are ongoing over the possibility of switching the match to Wembley.
A choice between London and Istanbul is expected within 72 hours.
“There are delicate negotiations that are going on at the moment,” Gove said on Sky News when asked about where the final should take place.
“My friend, my colleague the culture secretary Oliver Dowden is talking to people about this at the moment, and so I don't want to cut across that.
“But I'm sure that fans in the UK would dearly love to see the final played here in the UK.”
Wembley is due to host the Championship Play-Off Final on the same day as the Champions League Final but it is thought that the EFL is open to moving the match.