Lindor, 23, hit 15 home runs and had 78 RBI and 19 stolen bases in 158 games last season. He earned an American League All-Star nod.
"It's just one of those things we'll look at on a year-by-year basis," said David Meter, Lindor's agent. "I don't think it's very productive to draw a line in the sand."
Lindor hit .313 during his rookie campaign in 2015. He hit .301 last season and is hitting .351 through 14 games this season.
The shortstop is pre-arbitration eligible through 2018.
Brody Chernoff, son of Indians general manager Mike Chernoff, leaked the news of a possible Lindor extension in a March radio interview.
Apparently, the Indians were trying to extend Lindor in Spring Training. The six-year-old boy stated the team was trying to "get Lindor to play for seven years."
The Indians [8-7] face the Chicago White Sox [7-7] at 8:10 p.m. Friday at Guaranteed Rate Field in Chicago.