Swedish international Kacaniklic told fotbolskananelen that his Liverpool exit came about due to a case of mistaken identity by Hodgson.
The midfielder was transferred to Fulham as part of the deal to bring Paul Konchesky to Anfield, but Hodgson apparently quickly realised he'd made an error.
"When I was in Fulham, before I signed up, I had a conversation with Roy Hodgson on the phone where we found out he had transferred the wrong Alex," Kacaniklic said in the Lundh podcast.
"In his head, he thought he'd swapped another Alex for Konchesky. But by then it was too late. It's a little funny."
"He told me I was welcome back at Liverpool with open arms, but that I should do what I felt.
"I did not (go back to Liverpool). I had already changed my mind by then and was very excited about coming to Fulham.
"When Roy Hodgson came to the club it was different, a big change. Benitez had been there before and made the club his own with everyone who worked there. When he left, and took all his people with him, it became a bit turbulent.
"Hodgson didn't look so much at us younger players, he wanted quick results. He wanted Paul from Fulham."
The only other player with the first name 'Alex' in Liverpool's youth team at the time was Alex Cooper, who left one year later to join Ross County in Scotland.
The Fulham move worked out well for Kacaniklic - he became a starter while they were in the Premier League and broke into the Sweden national team at the same time.
Since then he had stints at Watford, Burnley, Copenhagen and Nantes before returning to his native Sweden this year with Hammarby, now aged 27.
