This is the first reported interest Gostkowski since he became available this offseason.
As of now, the Titans have Greg Joseph as the only placekicker on their roster.
Gostkowski, 36, is a former fourth-round pick of the Patriots back in 2006. He finished out his four-year, $17.2 million contract before agreeing to a two-year deal worth $8.5 million last year.
Gostkowski was set to make a base salary of $3.5 million for the 2020 season when the Patriots released him.
Gostkowski has played his entire 14-year career in New England.
In 2019, Gostkowski appeared in four games for the Patriots and converted 7 of 8 field-goal attempts (87.5 percent) to go along with 11 of 15 extra-point tries (73.3 percent).