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Former Green Bay star Rodgers is currently a free agent after leaving the New York Jets.
The 41-year-old would bring a wealth of experience to the Steelers - if only for one or two seasons.
Tomlin brought Rudolph back to the franchise earlier this year after a single season with the Tennessee Titans.
The Steelers decided to move on from last season's quarterback room, releasing both Russell Wilson and Justin Fields.
Rudolph has penned a two-year, $8million deal with the organization.
Although he is expected to be Rodgers' backup, Tomlin believes the former third round pick is good enough to be starter should the veteran opt for a move elsewhere.
“We’ve been in turnover in that [quarterback] room," Tomlin said.
"None of the guys from 2024 will be on our 2025 roster, but I think that’s one of the things that made Mason Rudolph such an attractive acquisition for us.
"We know his talents. He’s certainly capable. We like the intangible quality of him as a human and as a football worker.
"I just think the familiarity is very comforting."
Rudolph was drafted by the Steelers in 2018 in the third round.
He spent six seasons with Pittsburgh, mostly as backup, before joining the Titans last summer.
Rudolph went 1-4 in his five games as starter after taking over from Will Levis in Tennessee.
He ended the campaign with 1,450 passing yards, 9 touchdowns, and 9 interceptions for an overall 80.1 passer rating.
Pittsburgh remain hopeful of bringing in Rodgers, with ESPN insider Jeremy Fowler claiming it's either the "Steelers or retirement" for the former Super Bowl champ.
"I'm told - from the Steelers - that they do remain optimistic," Fowler said on Sunday.
"But nothing has changed from when Art Rooney, team president, addressed the media at the owners meeting on Tuesday.
"They feel good about this shaking out, that Rodgers will be a Pittsburgh Steeler.
"I have not got definitive word, but they're willing to wait 'a little while longer'.
