The Swede is out of contract at the end of the season, though Celtic hold the option of a 12-month extension to his current deal.
The 32-year-old has been with the Scottish champions since 2012 but has saw his role diminished slightly since January with the loan signing of Jeremy Toljan from Borussia Dortmund.
Asked about whether there was anything concrete in the reported interest from AIK, Lustig told the Daily Record: “Absolutely. They know well about my situation.
“I mean, I have been quite open that I might want to finish my career in Sweden. Clearly I think about it, but I have a lot to do.
“I will get a decision regarding the future next week.
“It has been hard for some time now when I do not know about the future. I have been here [Celtic] for seven years and me and my family enjoy it.”