Currie, who was signed for £250k from Brighton in December 2004, still has a year left on his current deal and Ipswich may want to cash in on the player who put in more crosses than any other championship player last season and was one of the division's leading players in terms of assists.
Currie has turned down Town's offer of a new deal and could leave on a free transfer next summer when his current one expires.
The Blues have indicated that they are also interested in the Whites former Brighton left-back Dan Harding and a swap deal may be agreed.
Magilton said in the East Anglian Daily Times: "Leeds have expressed an interest in Darren Currie and we have said we would be interested in a left-back.
"Danny Harding's name has come to the fore but that is as far as it has gone so far. Nothing has been made firm by Leeds and we have not decided anything."
Harding has a year left on his contract at Elland Road but was rarely used in the second half of last season following his high profile move from the south coast.