The Hammers brought the Argentine - who has sinced moved to Manchester United and Manchester City - to the club from Brazilian side Corinthians in the summer of 2006, but were later fined around €9 million (£5.5m) by the Premier League after being found to have broken rules regarding third-party ownership of players.
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The Hammers also subsequently agreed to pay over €40m (£26.5m) in compensation to Sheffield United after the Yorkshire club opened legal proceedings following their relegation.
And Sullivan has admitted that paying off that figure has damaged the club's ability to delve into the transfer market this summer.
"We have an eight-figure sum still outstanding over the Tevez affair, even though we have been paying it down over the past two years," he told The Mirror.
"That amount has to be paid off over the next 12 months, which does take its toll on our transfer activity."
However, the former Birmingham City chief praised manager Sam Allardyce's work in strengthening the squad in spite of his financial limitations.
"We've done some good business and brought in some real quality despite our still-limited resources," he added.
The summer arrivals have included experienced internationals Alou Diarra, Mohamed Diame, Modibo Maiga, Jussi Jaaskelainen and James Collins, all of whom, except Diarra, featured in Saturday’s 1-0 home win over Aston Villa.