The players formed a vital cog in Lille’s march to the Ligue 1 title in the 2010-11 campaign and have been linked with a host of clubs, including the likes of Arsenal and Liverpool.
"In my honest opinion, I want to keep those two boys," Garcia told Sky Sports. "With them fit and with a good attitude we can cause a surprise in Europe and do very well in the league.
"Hazard should stay, for me. He will learn more and improve again. In an ideal world, Gervinho would do the same with a new contract because he has one year left.
"The chairman and I are of the same mind, we should keep the two. We can accept one leaving, but not the two. It would be a nightmare for us."
Midfielder Hazard, 20, finished last season with seven goals and nine assists in 37 league appearances, while 24-year-old forward Gervinho scored 15 times in 34 matches in Ligue 1 and also provided eight assists.