Danny Holland and Jamie Jackson are likely to follow skipper Rob O’Brien, who has joined Farsley, out of the exit door at Horsfall Stadium.
Manager John Deacey has targeted some new signings but had said he was not looking for an influx of new players.
Replacing midfielders O’Brien and Jackson, plus forwards Holland and Tom Greaves, who is unlikely to return, would be his priorities.
Greaves enjoyed a spell on loan at FC United of Manchester last season, scoring goals that helped the Evo-Stik Premier Division outfit into the play-offs. Holland and Jackson have not renegotiated new terms.
Avenue’s finance director Kevin Hainsworth said: “Danny and Jamie were out of contract at the end of last season so they are free agents and I think they have been looking for new clubs.
"Both players were unfortunate with injuries last season and will want to be first-team regulars so they will probably move on.
“As with all the players who have played so well and so often for us, we wish them well.
“By the end of the close season, we will have three or four additions. Some discussions have already taken place but until the transfer window opens on July 1, we are not allowed to sign them on.
"We don’t want to reveal the names of the possible signings because that would be bad business and could alert other clubs.”
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