Leicester have been linked with the Argentinian forward all summer, with Brighton believed to have rejected three previous offers as they value the player at closer to £10m.
The 27-year-old moved to the south coast in January 2013 from Spanish side Almeria in a four-and-a-half-year deal for around £2m and he 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 its return to the Premier League.
City have so far brought in goalkeeper Ben Hamer, defender Matt Upson and midfielder Marc Albrighton, all on free transfers.