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But both have stated that they would be happy to sign new deals to stay at Glanford Park if they are offered.
38-year-old Beagrie was expecting to sign a contract extension at Christmas, but talks stalled when Chris Holland became chairman.
He told the Scunthorpe Telegraph: "Whether or not I will be at Scunthorpe next season is out of my hands.
"But whatever the scenario I would like to thank the Scunthorpe fans for their support of me, it's been unerring.
"Last year I took a 60 per cent wage drop so people know that it is not about money for me."
Record signing Steve Torpey also said that he wants to stay with the club.
He signed from Bristol City in January 2000 as the club tried to secure their Second Division status by bringing him in alongside Brian Quailey from WBA.