Meanwhile, Hull have not ruled out a move for Leicester centre-half Jack Hobbs, 22, who has been made available for loan by Sven Goran-Eriksson.
Current Hull boss Nigel Pearson signed Hobbs during his time with the Foxes.
But assistant manager Craig Shakespeare says that he is not a priority for them right now.
"As a coach and a manager you're looking to improve all the time," Shakespeare told BBC Radio Humberside.
Jack Hobbs is a player we know well and would fit the bill
Hull assistant manager Craig Shakespeare
"But we're very pleased with how Anthony Gerrard and James Chester are doing.
"We've also got Paul McShane who can play centre-back as well.
"Hobbs is a player we know well and would fit the bill but at the moment he's one we're monitoring.
"We haven't made contact with Leicester and we'll see if the situation arises where it's something we would possibly look at.
"We know about him, we know if he's available but would Leicester let him come to us? I think there's a question mark on that at the moment but we'll wait and see."
As for Folan, Shakespeare admitted: "I think several clubs have placed an interest.
"He's gone to have a look at them as much as them having a look at him and we've granted permission to do that."
The Republic of Ireland international became Hull's first-ever ?1m signing in 2007 when he joined the Tigers from Wigan Athletic.
He has made 64 appearances for the East Yorkshire club, scoring 12 goals, but has been hampered by injuries during his stay at the KC Stadium.
His last appearance came in the 1-1 draw at Barnsley on 30 October, when he suffered a knee injury in a collision with Tykes keeper Luke Steele.
Source: BBC Sport
Source: BBC Sport