Played for local club Eastwood for a while before being spotted by Stafford Rangers, then a good non-league side.  They progressed to the FA  Trophy final in 1972 as they beat Barnet 3-0 and his performance caught the eye of watching scouts.  Joining Plymouth Argyle, Aleksic failed to hold down a permanent place in the team and was put out on loan to Oxford United and Ipswich Town before leaving permanently for Luton Town, where he was managed by David Pleat.

Signed from the Bedfordshire club for £100,000, he was in competition with Barry Daines and Mark Kendall for his place in the Spurs side.  In fact during the 1980-81 season, Daines held the place between the sticks until the spring when he got an injury and Aleksic was in place for the run-in to the end of the season and the 100th FA Cup Final against Manchester City.  He starred in the semi-final against Wolverhampton Wanderers and was a winner with the team  at Wembley.

Not the luckiest of goalkeepers, Milija suffered two bad injuries in his time in goal for Tottenham.  He broke his jaw when clattered in the air by Joe Jordan of Manchester United at Old Trafford and in a Christmas game at Norwich City made a catch high at his post, but as he came down gashed his leg on a hook holding the net, which was protruding out.  Luckily, on both occasions, Glenn Hoddle took over in goal ... quite competently as it happens !!

After the FA Cup win, it looked as though Aleksic might have a good run in the side, but with Ray Clemence being replaced at Liverpool, Tottenham snapped up the experienced England keeper and Milija was relegated to the back up keeper.  His three and a half year stay with the club ended with a return to Luton and then a move to South Africa, where he took up a position as a coach.