"That (Olympics) is a dream for every athlete," Bedene was quoted as saying by British media.
"At the moment, I'm representing Great Britain but I do want to play at the Olympic Games.
"I don't know what the rules are, really. I haven't checked. I guess that means playing for the Davis Cup for them (Slovenia) as well."
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Bedene, who beat Harrison 6-4 6-0 3-6 6-1, faces Czech Jiri Vesely in the second round on Wednesday.
(Reporting by Aditi Prakash in Bengaluru)
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