The Blues forward has been linked with a potential move to La Liga giants Real Madrid at the end of the 2017-18 season.
Hazard has been regularly touted as a Real Madrid target since winning his first Premier League title at Chelsea FC in 2015.
The west London side have been unable to tie down the Belgium international to a long-term deal with 24 months left on his current deal.
Real Madrid manager Zinedine Zidane will be looking to improve his squad following a disappointing domestic campaign.
Former Chelsea FC winger Nevin warned the Blues that the west London side will need a drastic overhaul should Hazard leave for Madrid.
“Hazard has been pivotal to most of the things Chelsea have done well,” Nevin told BBC Radio 5 Live.
“If you lose him, you change everything. Most of the good things go through Hazard.”
Hazard has scored 12 goals and has made six assists in 34 games in the Premier League this season to finish in fifth place in the table.
The Blues were 1-0 winners against Manchester United in the FA Cup final at Wembley after Hazard scored the winner from the penalty spot.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news