United have been heavily linked with a move for Clyne as Louis van Gaal looks to strengthen at right-back in the off-season.
Clyne has helped Southampton to fifth place in the Premier League table this season, but claims that his ambitions stretch beyond playing in the Europa League next term.
I'm an ambitious person and want to try and win the title and play in the Champions League.
Nathaniel Clyne
He said: "I'm an ambitious person and want to try and win the title and play in the Champions League.
"It's nice to hear teams are interested in you."
Last week Saints boss Ronald Koeman admitted that the south coast club may struggle to retain Clyne's services this summer.
He said: "We are still trying to keep Clyne in the club.
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Nathaniel Clyne wants Champions League football
"We know it's not easy as maybe there is some interest.
"At the moment, there is not a serious bid for whichever player in the team, but we'll do everything to keep them."
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