Ter Stegen, 28, has two years left on his Barca contract but is struggling to agree a new deal.
Speaking on Què T’hi Jugues!, journalist Santi Ovalle said: “Barca’s board of directors are more optimistic than Ter Stegen’s camp.
“However, both parties have the will for the German goalkeeper to renew [his contract].”
He added that Ter Stegen has offers from major European clubs that make a contract agreement even more difficult.
His colleague Cristobal Chassaigne later commented that the clubs ‘seem to be Chelsea and Bayern Munich’.
Chelsea are actively seeking a goalkeeper following Kepa Arrizabalaga‘s dreadful season.
The Londoners are ready to sell or loan out Kepa and replace him between the sticks.
A move to Bayern seems more improbable with Manuel Neuer still the established number one, and Alexander Nübel arriving in from Schalke.
Ter Stegen has been an excellent performer for Barcelona since his €12m move from Borussia Monchengladbach in 2014.
The German international has kept exactly 100 clean sheets in his 234 appearances for Barca.