Tottenham made a verbal offer of up to £40million including add-ons for Chelsea midfielder Conor Gallagher.
The bid is £5m short of Chelsea's valuation of £45m for the 23-year-old.
As Mail Sport reported yesterday, the England international is weighing up his future after Chelsea brought in Cole Palmer, Moises Caicedo and Romeo Lavia for their midfield.
Gallagher captained Chelsea against AFC Wimbledon and would prefer to stay if he continues to get regular game time but is realistic about his opportunities.
Despite the influx of talent at the Blues this summer, Mauricio Pochettino has started the academy graduate in all three of the club's Premier League fixtures so far this season.