The 19-year-old defender is widely regarded as one of the brightest young talents in France at the moment, and has attracted attention from a number of different clubs.
Newly-crowned Ligue 1 champions Paris Saint-Germain are believed to be monitoring the France U20 international's development, but it's the Premier League duo who look most likely to go for his signature this summer.
Chelsea are still on the lookout for a long-term successor for Ashley Cole, and despite the fact the west London club recently offered Ryan Bertrand a new contract they are still considering an attempt to lure Digne to Stamford Bridge.
However, the Blues could face competition from Liverpool, as Brendan Rodgers looks to add to his Anfield ranks when the transfer window reopens on July 1.
Rated at around £10million, it's not yet clear whether either side will be willing to meet Lille's valuation of the talented teenager, but must pay top dollar for the exciting young prospect.