Transport minister Grant Shapps said supporters should not travel to Turkey for the final between Manchester City and Chelsea and those who do will be subject to compulsory hotel quarantine.
Turkey is currently in lockdown until 17 May and ranks fourth globally in the number of daily Covid-19 cases.
Uefa is understood to be in discussions with the relevant Turkish authorities in regards to the logistics of hosting the final, although the British government has previously allowed elite sportspersons to travel to and from red list countries.
The final is due to take place on 29 May at the Ataturk Olympic Stadium in Istanbul and Turkish football authorities had hoped 4,000 British fans from each side would make up part of a 25,000 capacity crowd.
Shapps said the government would be willing to host the match amid further calls for Uefa to allow common sense to prevail.
“I’m afraid we are having to put Turkey on the red list,” he said in regards to the final. “This will have a number of ramifications. First of all, it does mean with the regards to the Champions League, fans should not travel to Turkey.
“The FA are in discussions with Uefa on this. We are very open to hosting the final but it is ultimately a decision for Uefa.
“Of course the UK has already got a successful track record of football matches with spectators, so we are well placed to do it.
“We are very open to it but it is in the end a decision for Uefa to make, but given there are two English clubs in that final, we look forward to what they have to say.”
Uefa had previously been insistent the final would go ahead as planned in Istanbul and stated earlier this week that it had no plans to change the venue.
“The Uefa Champions League final will take place in Istanbul on 29 May with a limited number of spectators and we are assured the temporary lockdown which is in force until 17 May should not have any impact on the match,” the governing body said in a statement.
“Uefa continues to work closely with the Turkish Football Federation and the local and national authorities to stage the match safely.”