French forward Dembele ruptured a hamstring tendon last week and will undergo surgery next Tuesday in Finland, after which Barca will determine how long he will be out for.
Spanish soccer federation (RFEF) rules dictate that if a player is injured for at least five months then their club can sign a replacement outside a transfer window, as long as they are based in Spain's top two divisions or a free agent.
The injured player is not allowed to play again for the team before the five-month period has elapsed and must agree to the arrival of the new player.
Dembele's injury has left Barca with only three natural forwards in talisman Lionel Messi, Antoine Griezmann and 17-year-old Ansu Fati as Luis Suarez is out until May after undergoing knee surgery.
"If it's possible, we want to sign a player who is versatile. It's not easy, right now the market is closed and we need to get the request approved first of all," Setien told reporters ahead of Barca's La Liga game at Real Betis on Sunday.
"It's obvious that we need a player to come in and that they would help us out."
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Reports in the Spanish media say they are looking at bringing in either Real Sociedad forward Willian Jose or Getafe's Angel Rodriguez.
Barca are second in La Liga, trailing leaders Real Madrid by three points and were eliminated from the Copa del Rey on Thursday following a 1-0 defeat by Athletic Bilbao.
Sunday's game will see Setien make his return to Betis since being sacked by the club last May after two seasons, during which he led the club into Europe but was also the subject of fierce protests by fans.
"I spent two marvellous years there and I only have words of gratitude because they gave me the opportunity to grow," added Setien.
"I remember the success we had at certain stages and how much courage we had. The last few months were tough but I don't feel any bitterness towards anyone."
In addition to missing Suarez and Dembele against Betis, Barca will be without suspended defender Gerard Pique.