Xia, who became the first mainland Chinese to fully own an English team, made clear his vision for the club, who were relegated from the Premier League last season.
"I hope in five years, or after five years, we will talk of this club as Madrid or Barcelona," he told the BBC.
"Or someone else as well known and accepted by people in the world to say 'oh, that's the greatest club'".
The former European Champions appointed Roberto Di Matteo as their new manager earlier this month as they eye an immediate return to England's top-flight.
"I know it will be difficult," Di Matteo, who guided Chelsea to the Champions League title in 2012, told British media.
"It's a rebuilding job and I have to turn things around. The objective is to get promotion this year.
Xia had earlier told Reuters that the club would spend about 30-40 million pounds on players next season, with British media reports suggesting that Bournemouth defender Tommy Elphick would be the club's first signing under Di Matteo.
"We need to turn a team that has struggled into a strong competitive team. All aspects need to be looked at," Di Matteo added.
"We need a united group, people who are willing to fight for the club in the Championship. But, with the right personnel we can do well."
($1 = 0.7060 pounds)
(Reporting by Nivedita Shankar in Bengaluru, editing by Pritha Sarkar)
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