The Premier League newboys have been linked with the Argentinian forward all summer, with the Seagulls believed to have rejected at least three previous offers.
The 27-year-old moved to the south coast in January 2013 from Spanish side Almeria on a four-and-a-half-year deal for around £2m and has scored 26 goals in 58 appearances.
If the offer is accepted, the deal would break Leicester's club record transfer fee of £5m spent on Ade Akinbiyi in 2000.
Leicester boss Nigel Pearson has not ruled out making a "marquee signing" this summer, but has rejected reports he will spend big as he prepares his squad for their return to the top flight.
City have so far brought in goalkeeper Ben Hamer, defender Matt Upson and midfielder Marc Albrighton, all on free transfers.