Valued at £32m by his club, Athletic Bilbao, Laporte has had Chelsea and Arsenal scouts at his games with both Premier League clubs eyeing defensive reinforcements when the January transfer window reopens in six weeks time.
The Daily Express reports that Arsenal were prepared to make Athletic an opening offer to sign the Frenchman, but it has since been reported by the same newspaper that Chelsea are also keen.
Jose Mourinho has been heavily linked with a move for his former-Real Madrid player Raphael Varane while Arsenal were reportedly considering a bid for Borussia Dortmund centre-back Mats Hummels.
Dortmund manager Jurgen Klopp is desperate to keep Hummels, and it looks unlikely the German international will leave until next summer at the earliest - if at all.
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Chelsea's interest in Varane has taken a step back after the Blues were quoted too high an asking price for the French international. They believe they can get a better deal for Laporte, another rising French star.
The 20-year-old moved to Athletic from Bayonne in 2010 but only made the step up to the first-team two years ago. Since then the versatile defender (he can play left-back and centre-back) has gone from strength to strength, winning eight under-21 caps with a full national team cap on the horizon.
Chelsea & Arsenal
Chelsea are preparing for a future without club captain and defensive lynchpin John Terry. They have Kurt Zouma, signed from St Etienne, knocking on the door but Mourinho wants options in defence.
As for Arsenal, they desperately need to make one or two additions to bolster a back-line that has featured Nacho Monreal at centre-back far too often already this season. Thomas Vermaelen, who left for Barcelona, has not been replaced.