The 25-year-old departed Highbury last month after making more than 200 appearances for the Cod Army.
He was sent out to Bury on loan at the start of the season, where he impressed, and, upon recovering from a hamstring injury, was immediately released by Graham Alexander's side.
When asked about his exit from Highbury by Shrimps player, Beeley cryptically said: "I won't go into too much detail. I wouldn't say it's particularly from football but things happen in football and I'm just going to leave it at that.
"My time there was great, there's a great set of fans and they were always supporting me. I've got a lot of appreciation for the fans at Fleetwood and hopefully I'll have as much for the Morecambe fans."
Beeley immediately ended up with Sky Bet League Two rivals Morecambe, whom he signed a contract with until the end of the season.
He made his debut in Saturday's 1-0 defeat to Burton but the right-back was non-committal on whether he sees his long-term future at the Globe Arena.
"I will see what my options are," he noted.
"I'll speak to the gaffer and see what his thoughts are, (the decision is) not entirely mine. Hopefully I'll do well until the end of the season and see what comes of it."
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