The west London side finished in fifth spot in the Premier League table under Antonio Conte last season to miss out on a Champions League place for the second time in three seasons.
Chelsea FC did end the campaign with a trophy following a 1-0 win over Manchester United in the FA Cup final at Wembley thanks to Hazard’s winner from the spot.
The Blues finally sacked Conte at the start of July before Chelsea FC appointed controversial Italian head coach Maurizio Sarri ahead of the new Premier League season.
Sarri has already signed Napoli midfielder Jorginho and veteran England goalkeeper Rob Green in the summer transfer window ahead of Thursday’s 17:00 BST deadline.
Alvaro Morata’s future at Stamford Bridge has been a source of speculation amid reported international from Serie A, including his former employers Juventus.
Former Manchester United defender Neville believes Chelsea FC need to sign a new centre-forward as well as keep Hazard to challenge champions Manchester City next season.
“Chelsea look like they are moving,” Neville told Sky Sports.
“They have been a little slow in the transfer market and a little bit less obvious in the transfer market over the last few years than they have been previously.
“It looks like they are making a move again. To win the league they have to keep Eden Hazard and get a centre-forward. Alvaro Morata is a good player but I think about the void left by Diego Costa. If they are going to play a single striker, which they historically have, then they need another one.”
Chelsea FC finished behind Manchester City, Manchester United, Tottenham Hotspur and Liverpool FC last term.
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