"It could be a mess," the 48-year-old told reporters on Wednesday. "Let's say if two of our teams made it to the Champions League final then we wouldn't see them, at best, until the Monday before we play on the Thursday.
"And with the emotion of (the Champions League final), can those players even realistically play on the Thursday night for us?"
Manchester United, Tottenham Hotspur, Manchester City and Liverpool are in the quarter-finals of the Champions League, the first time since 2009 that four teams from England's top flight have reached the competition's last-eight.
Southgate's squad for this month's European Championship qualifiers has 13 players from the four clubs, including Spurs striker Harry Kane, Liverpool captain Jordan Henderson and City winger Raheem Sterling.
"They would all need a period where they would need to psychologically switch off," Southgate added. "We'd have to look at Champions League final players when we get to it.
"It will be a little bit like the World Cup in that players will finish at different times."
England face the Czech Republic at Wembley on March 22 followed by a trip to Montenegro three days later.
(Reporting by Rohith Nair in Bengaluru, Editing by Simon Jennings)
