The Foxes reportedly had offers of £6.5million and £7.5million turned down by the Championship club, and are now set to make their final play for the striker, according to the Watford Observer.
Leicester broke their club transfer record this season to sign another centre-forward in Brighton and Hove Albion's Leonardo Ulloa. That deal was worth £8million, potentially rising to double figures, and it is believed that Deeney would command a similar fee.
Nigel Pearson's side are looking to strengthen their attack as they hope to maintain their Premier League status beyond next season, but it is debatable whether splashing the cash on another front-man would be the right move.
The Foxes already boast an impressive strike-force in Ulloa, Jamie Vardy and Dave Nugent. The trio scored a combined 54 goals in the Championship last season, with Nugent bagging 22 and Ulloa and Vardy netting 16 each.
Leicester recently came to an agreement on a new contract with Nugent, and are in talks to extend Vardy's deal before the season starts. They have also signed talented young striker Jack Barmby from Manchester United.
Deeney has been prolific for Watford in recent years - he scored 45 goals in the past two seasons - and his athleticism and finishing ability should stand him in good stead in the Premier League.
The ability to score goals is of course crucial in the Premier League, but perhaps even more important is a solid defence.
Of the teams promoted to the Championship prior to last season, the two teams who managed to stave off relegation - Hull City and Crystal Palace - had far superior defensive records than Cardiff City, who finished bottom. Cardiff conceded 74 goals, compared to Hull's 53 and Palace's 48.
In attack, the three sides were not dissimilar, Cardiff scored 32 goals, Palace 33 and Hull 38. What separated the three promoted sides was not their attacking firepower, but their ability to defend.
With the aging Matthew Upson Leicester's only new arrival at the back this summer they would perhaps be better off spending their cash on defensive reinforcements than on another striker.