"We are evaluating everything and we just gotta keep moving forward," Gettleman said Wednesday in Indianapolis.
The Giants were 5-11 in Gettelman's first season as the team's general manager in 2018. Manning, 38, completed a career-high 66 percent of his passes for 4,299 yards, 21 scores and 11 interceptions. He posted a 92.4 quarterback rating.
The two-time Super Bowl champion and four-time Pro Bowler is playing on the final season of a four-year, $84 million contract. Manning is set to make $17 million in his 16th season and has a $5 million roster bonus due in March.
Several mock drafts have the team selecting a quarterback in the first round of the 2019 NFL Draft, including the UPI mock draft, which has the team selecting Missouri's Drew Lock at No. 6 overall. Other mock drafts have the Giants targeting Ohio State quarterback Dwayne Haskins.
"I think Eli can help us win games," Shurmur said. "He proved when the players around him started playing better, that he can play at a very high level and help us win games."
"At this point, I want Eli back. He's back and ready to go."
Gettleman said he had a conversation with Manning after the season ended. He also said you can look at a number of examples where a team had a veteran quarterback and they drafted a young player and at some point in time "the torch got passed."
He also would not rule out a veteran.
"I can't say anything like that," Gettleman said. "You don't know what's going to happen. You don't know."