Born in Sheffield, Eckhardt grew up supporting his hometown side Sheffield United and later joined the youth system at the club as a teenager. After a number of reserve team players were required to travel with the first-team, Eckhardt was handed an opportunity to play for the reserves against Coventry City, during which he impressed enough to be offered a two-year deal by manager Martin Peters. During the 1985–86 season, he was roommates with Ray Lewington who promised Eckhardt that when he became a manager he would sign him for his team, fulfilling the promise two years later when Lewington took charge of Fulham. Although he turned down Lewington's initial approach in 1986 as he was playing regularly for the first-team, he later accepted the move in November 1987 after being dropped, joining for a fee of £50,000.