The 26-year-old has played in his Serbian homeland, Armenia and Russia and earned a move to FC Tosno in the Russian top division.
However, they went bust and all of their players became a free agent earlier this season.
And Dugalic claims he came extremely close to signing for the Ibrox club.
The former Radnicki Nis stopper recalled: “Steven Gerrard is my absolute idol in football and I almost signed for him at Rangers.
“When I played for Tosno, I was contacted by Gerrard to go and play for his Scottish team.
“For the transfer to go through, I was told Rangers wanted to run it past all 11 of their scouts before they gave it their approval.
“Ten of them approved me, but one didn’t and the transfer never went through. Instead an offer came to sign for Kairat Almaty in Kazakhstan and I went there instead.”