Chelsea made a £40 million bid for Modric at the end of the summer transfer window in 2011, according to the Independent, but Spurs stood firm and kept hold of the technically-gifted midfielder for one more season.
However, Jenas - writing in his latest Yahoo column about the respective predicaments of West Brom striker Saido Berahino and Everton defender John Stones - claims Modric had his heart set on a move to Stamford Bridge.
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Talking about the situation involving Chelsea target Stones, Jenas wrote: “It reminds of when Chelsea made repeated bids for a team-mate of mine at Tottenham, Luka Modric.
“He was adamant that he wanted to go, but after Daniel Levy refused to sell him he got over it very quickly and it didn't affect his form at all.
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“He remained professional, stayed the whole season and played a key role - finally getting his move to Real Madrid the following year.
“But it takes a certain type of person to be able to do that, and it's also a risk. You're relying on making it through that season unscathed and maintaining your form.”
Jenas dishes the dirt on Berbatov
Jenas compared the professional attitude of Modric to that of another former teammate, Dimitar Berbatov, who joined Manchester United in 2008 from Spurs.
“He'd come out for training but he'd just be walking around. Before anyone points out that was just standard Berbatov, this was different. It was Berbatov in ultra-chilled mode,” Jenas added.
“He wouldn't talk much or really smile at anyone, he would literally just stand around. Essentially he was just turning up to training to avoid getting fined, and his message to the club was pretty clear: you can tell by the way I'm training that you're not going to get anything out of me, so just let me go to Man Utd.”
A rare insight
Jenas’ latest column certainly provides a rare insight into how footballers might behave on the training ground when they want to leave their current employers.
There is now less than a week to go before the summer transfer window closes and both Berahino and Stones could secure moves to Tottenham and Chelsea, respectively.
Chelsea fans: how good would Luka Modric have been at Stamford Bridge? Have your say by leaving a comment in the box below!