Lennon joined Everton on-loan last month to the end of the season.
The London Evening Standard says Lennon is keen to seal a permanent move to the Blues in the summer.
He earns about £55,000 a week at White Hart Lane, and it is believed Spurs are contributing to his salary for his stint at Goodison Park. That obligation would end were he to leave north London permanently, meaning Everton would have to increase their offer.
Tottenham's asking price of £7 million is also believed to be too steep for a player about to enter the final year of his current deal.
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