The 60-year-old music mogul wants the chart-topping boyband to make their comeback appearance on 'Britain's Got Talent', but James hopes they'll first appear on 'The Late Late Show', if they do decide to reunite.
A source said: ''Cowell and Corden are now in a battle for who gets One Direction to perform together again first.
''Simon was their mentor who first had the idea of putting them together as a group and they are one of the most successful acts from one of his shows.
''But while all the One Direction boys adore Simon and enjoy working with him, there are other TV shows today.''
Harry Styles is reportedly leaning towards the band - which also includes Liam Payne, Niall Horan and Louis Tomlinson - making their return on James' show.
The insider told the Sunday Mirror newspaper: ''Harry Styles is very good friends with James's executive producer Ben Winston - he even used to live with him - so his inclination is to lean towards James's show.
''The other lads really like James and Ben too and the show is a great platform for them. It's a tough call.''
Liam, 26, recently revealed the band are keen to do something together to mark their ten-year anniversary - although he didn't discuss specific plans.
He shared: ''I''m not allowed to say too much obviously because I would be giving it away.
''We've been speaking a lot more at the moment, I think we are all feeling that that ten year ... it's a very special moment.''
At the moment, it remains unclear whether Zayn Malik - who quit the group in March 2015 - would be interested in reuniting with the band.
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