Delroy Facey was signed by Allardyce at Bolton Wanderers in 2002. He made 10 Premier League appearances for the club in two years, scoring one goal.
He is among the six men to have been arrested as part of a National Crime Agency investigation into alleged match fixing - linked to Asian betting syndicates - in non-League football in England.
"You can tell I'm shocked by my reaction," Allardyce told the Daily Mail. "I'd heard the news on the radio while driving this morning but I didn't realise any names had been linked. Wow.
"I remember Delroy. He did well against us for Huddersfield in a cup game and we did the usual thing, getting our scouts to keep an eye on him.
"He didn't quite make it to the top but I thought he had a good career. He might have been frustrated that he wasn't as successful as he wanted to be. He was a powerhouse. Lots of pace and strength.
"But what we found with him was the simple fact that he couldn't score enough goals at the Premier League level. He was prolific in the lower leagues. But not with us."
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