Iniesta, 33, has spent his entire career at Barca but said last week he has received an offer to play in China and must decide by the end of April whether he takes it or remains at the Nou Camp.
"It's a personal decision and everyone hopes he stays at Barca because he's a great person. We know that we have to keep going as a team until the end of the season and we need him right now and for many more years," Ter Stegen told reporters after Barca went 11 points clear at the top of La Liga.
"We are thinking about the present and he'll make the decision. I hope he stays but the only person that knows what to do is him."
Iniesta began the game against Athletic on the bench after revealing in the aftermath of Wednesday's 3-0 win over Chelsea in the Champions League that he had received the offer from China. He was greeted with chants of "Iniesta please stay" when he replaced Ousmane Dembele shortly after the hour mark.
"We know he's a great person who knows he is very important for the club and we'll try everything to convince him to stay," added Ter Stegen.
"It's a personal decision and we're going to support him whatever he does. We love him as a captain."
Barca coach Ernesto Valverde added: "For now all we can do is wait and see what he decides to do. We know what he gives us and we would all like to have Iniesta around forever."
Iniesta made his Barca debut in 2002 and has lifted eight Liga titles, five King's Cups and four Champions League titles with the Catalans, who could win a third treble this season.
Barca lead nearest challengers Atletico Madrid by 11 points after Diego Simeone's side lost 2-1 at Villarreal on Sunday. They play AS Roma in the Champions League quarter-finals in April and meet Sevilla in the King's Cup final on April 21.
(Reporting by Richard Martin; Editing by Christian Radnedge)
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