CLEVELAND, Ohio - Bryan Shaw, the busiest reliever in the big leagues over the last five years, is not expected to be back with the Indians next year.

The Indians, it has been learned, don't think that they will be able to compete with the kind of offers Shaw is expected to receive this winter on the free agent market. Shaw and five other Indians will be free to field bids from other teams on Tuesday.

Shaw has made more appearances than any big-league reliever in the last five years. He's pitched in 378 games, all with the Indians, in that time. He was acquired from Arizona along with Trevor Bauer in a three-team trade in December of 2012.

The Indians have had one of the top bullpens in baseball over the last several years. The cost of keeping that pen intact has grown. Closer Cody Allen is expected to make an estimated $11 million through arbitration this winter. Set-up man Andrew Miller, entering the last year of his deal, will make $9 million this year.

Shaw made $4.6 million this season. He's expected to be in line for a three or four-year deal worth an estimated $8 million a year.

If the Indians tried to keep Shaw at those prices, it would mean they'd be paying their top three relievers close between $28 million and $30 million in 2018.

Shaw, 29 on Wednesday, has never been on the disabled list and should be a hot commodity on the open market. As manager Terry Francona said at the end of last season, "If he doesn't come back, it will take two guys to replace him."

Last year St. Louis signed left-hander Brett Cecil to a four-year $30.5 million contract. He appeared in a career high 73 games, going 2-4 with a 3.88 ERA in 67 1/3 innings.

Shaw made 79 appearances last season, going 4-6 with a 3.52 ERA in 76 2/3 innings. Kansas City's Peter Moylan and Shaw tied for the AL lead in appearances this year. Shaw led the league outright in 2014 and 2016 with 80 and 74 appearances, respectively. He is the only Indians pitcher to appear in 70 or more games in five seasons.

"He is the most consistent human being I've ever seen," said Allen.

Allen ranks first in franchise history with 386 appearances. Shaw is second with 378.

If Shaw does not return, who will replace him? It could mean more work for relievers such as Dan Otero, Nick Goody and Zach McAllister. They all made 50 or more appearances last year, but were left off the roster for the AL Division Series as the Indians kept three starters in the in the bullpen in Josh Tomlin, Mike Clevinger and Danny Salazar.

It could mean more opportunities for right-hander Shawn Armstrong, who bounced between Cleveland and Class AAA Columbus nine times this year. The same goes for left-hander Tyler Olson, who made 30 appearances as a rookie last season without allowing an earned run.

The Indians could increase their efforts to sign Joe Smith. Like Shaw, Smith is one of the Tribe's free agents. They acquired him at the July 31st trading deadline from Toronto.

Smith went 3-0 with a 3.33 ERA in 59 appearances with Toronto and the Indians this year. He struck out 71 and walked 10 in 54 innings.

Shaw, in fact, appears to be following a career path blazed by Smith. From 2009 through 2013, Smith appeared in 303 games for the Indians. After the 2013 season, he turned free agent and signed a three-year $15 million deal with the Angels.

The Indians could also move Salazar into a late-inning relief role. He certainly has the velocity, but his durability and strike-throwing ability is questionable.