Central defender Jahic, who has 31 caps for Bosnia, arrived in Perth last Thursday as he searches for a club following his summer exit from Turkish top-flight side Karabukspor.
And Wright could make an offer after telling Martin Woods, the former Leeds, Rotherham and Doncaster midfielder, that he did not have the funds to sign him as well following his trial spell.
Wright said: "Sanel is still in and Martin has gone back. I would have liked to have signed him, he was excellent when he was here, but my priorities are defensive cover.
"We have Sanel in for another couple of days and we'll make a decision on that at the weekend.
"I wouldn't have the funds to do both. Ideally I would have liked to have kept Martin. He's a quality player, he came in for a few days and was really fit.
"I couldn't really keep him hanging on. He has a couple of opportunities down south and we wish him well. I have no doubt he'll get a club because he's an excellent player."
Jahic would provide additional defensive cover for Wright as Steven Anderson is likely to be out until the turn of the year after being told the dislocated thumb he suffered against Partick on September 28 will take time to heal.
Wright added: "The surgeon saw him on Monday and he did say it would be a minimum of eight weeks to three months and he is now saying it looks more like it will be three months.
"There is not a lot we can do about it; we are fortunate Gary Miller has come in and done well."
Meanwhile, St Johnstone have agreed a deal with Queen of the South to allow goalkeeper Zander Clark to leave on a short-term emergency loan deal.
Queens hope to register the 21-year-old ahead of their Scottish Championship clash with Dundee.