document: Bedene, 27, became a British citizen in 2015 but has been unable to overturn a ban preventing him from representing Great Britain in the Davis Cup.
  To go to the Olympics, a player must have been available for the Davis Cup.
  "That's a dream for every athlete," said Bedene after beating Ryan Harrison to reach the French Open second round.
  Bedene represented Slovenia in three Davis Cup ties before becoming a British citizen - and rules were introduced shortly after his switch barring players from representing more than one nation.
  "I'll have to see what can be done," he added. "At the moment I'm representing Great Britain, but I do want to play Olympic Games."
  Bedene moved to Britain in 2008 but Dan Evans said earlier this month he still considered himself to be the British number three despite being overtaken by Bedene in the rankings.
  "At the moment, for the clay season, I spent quite a lot of time in Slovenia," Bedene said on Monday.
  "My fiancee said she wants to move back. She wants to have her career there.
  "I'm travelling a lot, so it's not easy - but I do want to spend as much time as I can with her.
  "I've still got a house in England. My home is still there. I have always been known as Slovenia-born - but I love Britain.
  "I feel Slovenian and British."
  BBC tennis correspondent Russell Fuller
  Bedene would need to play three Davis Cup ties for Slovenia between now and the Tokyo Olympics to be eligible for the 2020 Games, and so realistically would need to switch back in time for the 2019 competition.
  He has a Slovenian passport, but also needs to be in "good standing" with the country's Olympic Committee and would have to rebuild relationships broken when he started playing under the British flag.
  In March, an arbitration hearing upheld the International Tennis Federation's ruling that players can no longer represent more than one country, but expressed the hope the governing body could one day be persuaded that Bedene is worthy of an exemption.
  That appears a long shot in the time available, and any switch back to Slovenia is likely to go down very badly with those at the Lawn Tennis Association who have spent so much time and resources on his case.
  Media playback is not supported on this device
  Earlier on Monday, Bedene won 6-4 6-0 3-6 6-1 against American Harrison - a player ranked 10 places higher at 42 in the world.
  Afterwards, he accused his opponent of "tanking", saying the American effectively gave up the second set to help him win the third
  "That is in a way a tactic, and it worked," Bedene told BBC Sport. "That was his decision. I'm not doing that.
  "It's never easy to start off the third set after someone's tanking."
  Bedene has now won 21 of 24 matches on clay this year, winning two titles on the second-tier Challenger circuit and reaching an ATP Tour final in Hungary.
  He will face Czech player Jiri Vesely in the second round, with Rafael Nadal of Spain a potential fourth-round opponent.
  Fellow Britons Andy Murray, Kyle Edmund and Johanna Konta start their challenge on Tuesday, but Dan Evans lost on Sunday.
summary: British number three Aljaz Bedene is considering switching his allegiance back to Slovenia in order to compete at the Olympics.