Taylor died in January this year aged 72 and the allegation centres on his spell in charge of Aston Villa, the club he managed from 1987 to 1990.
Villa sacked scout Ted Langford in 1989 after learning of sexual abuse allegations against him but did not alert police, the BBC reported in January.
Langford had joined the club from Leicester two years earlier. He was jailed for three years in 2007 for sex offences against young footballers and died in 2012.
In an interview with the BBC’s Victoria Derbyshire show, former Leicester defender Tony Brien said that as a teenager he warned Villa about Langford’s behaviour.
But he said Taylor then told him: “Look, you’re a young lad starting out in the game. I know you’ve just made your debut (for Leicester). Could you really be dealing with all the obscenities from the terraces? So I just suggest you sweep it underneath the carpet.”
Brien was upset by Taylor’s comments, and said of the experience: “I went into the kitchen where my mother was still doing the washing-up and she said: ‘Well?’ And I just told her: ‘They told me to sweep it underneath the carpet’, and I broke down in tears.
“I knew I couldn’t live with it for the rest of my life so I went to adults who I trusted, who I thought would do something about it. But that was their reaction to me.”
Brien claimed in January that he had made several attempts to warn Taylor’s then assistant manager Dave Richardson about Langford. The defender was 18 at the time and had seen Richardson leave Leicester for Villa, with scout Langford going with him.
Richardson has strongly denied he advised Brien not to go public, and in January he said in a statement released by lawyers: “I cannot recall ever having a conversation with him about any allegations of abuse.”
Brien said he experienced abuse at the hands of Langford when playing for youth side Dunlop Terriers between the ages of 12 and 14. Dunlop Terriers were managed by Langford and served as a feeder side for Leicester and later Villa.
Brien, who waived his right to anonymity to speak about his ordeal, reportedly told Villa in the 1987-88 season that he knew from personal experience that boys were at risk.
According to the Guardian, the independent inquiry is also looking at a separate allegation that another of Langford’s victims came forward with information and that he too was discouraged by Taylor from pursuing the matter.
Villa have not yet commented on the specific allegations regarding Langford, but told the Guardian: “The club now has robust safeguarding polices and procedures in place to deal with any new and historic complaints raised.”
Taylor left Villa to become England manager and led the team at Euro 92 before departing after a failure to reach the 1994 World Cup. He also managed Lincoln, Watford and Wolves in a management career spanning over 30 years.