The news comes as disgraced former football coach Bennell was convicted at Liverpool Crown Court of a total of 43 counts of child sex abuse against 11 victims.
Speed's name was linked to the case when one victim, who Bennell had pleaded guilty to abusing in 1998, said he knew of four men who had been coached by him - including Speed - who had gone on to take their own lives.
However, Speed's family has now spoken out to say that the Welshman, who passed away in 2011, knew nothing about the abuse and was not among Bennell's victims, though he was contacted by police during the investigation.
A statement issued on behalf of Speed's family by the League Managers Association (LMA) on Thursday night said: "In light of recent speculation, we would like the following points to be made quite clear.
"1. Gary Speed was interviewed on two occasions by the police during their investigations into allegations made about Barry Bennell.
"2. On both occasions Gary made it quite clear that he did not know anything about Bennell's alleged behaviour and also made it clear that Bennell had never behaved inappropriately towards him.
"3. The police have subsequently made clear that they were satisfied that there was no reason to link the Bennell investigation to Gary.
"4. The prosecution also made clear at the trial of Bennell that "there was no evidence called at any of the inquests suggesting that [his] death was linked to" Bennell."
Bennell, 64, who holds previous convictions for similar offences, will be sentenced on Monday for abusing 12 boys following his latest convictions for offences against youth footballers between 1979 and 1991.