Colombia star Rodriguez joined Real Madrid in a deal reportedly worth €80million in July after winning the golden boot at the FIFA World Cup in Brazil.
The 23-year-old led Ligue 1 in assists last season, helping Monaco finish second to Paris Saint-Germain.
Jardim said he wanted to find a replacement of similar quality who could make his team stronger.
"Of course, James was a very important player last season but we can't count on him now," Jardim said on Friday.
"We need to look for a replacement that will be of the quality to take that place and make the team stronger."
Despite losing several players in the close-season, including Rodriguez, Jardim said he believes Monaco have a better team than PSG.
"I do believe that Paris Saint-Germain are a strong candidate for the French league as they have a very reinforced team, but I believe that Monaco are better," he said.