The Sun reports that Ranieri has made an offer of £1.5m for the Leeds full-back, who turned down a move to another Spanish club, Villarreal, last week.
Harte, 26, has two years left on his £25k-a- week deal at Elland Road and The Whites are keen to offload him as it would save them £2.8m on wages.
New signing Danny Pugh is the favourite for the left back spot next season.