Le Normand, 27, has been linked with Newcastle, Napoli and Atletico Madrid.
Now Spanish journalist Ruben Uria states that all three clubs have tabled their bids to Real Sociedad.
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Le Normand has made 37 appearances and scored two goals in all competitions for Real Sociedad this season.
Atletico Madrid coach Diego Simeone is said to be looking for new options for the centre-back position this summer.
Atletico Madrid have made a bid of 20 million euros, plus Javi Galn .
The left-back is currently on loan at Real Sociedad - who are said to be keen to keep the player permanently.
Newcastle have offered Real Sociedad 25 million euros plus 5 million in bonuses. Napoli's bid is said to be 27 million euros plus 5 million in bonuses.