The Luxembourger revealed the news while responding to criticism of the Enstone team's other driver, Pastor Maldonado, who is enduring an horror 2014 season.
Having switched his lucrative PDVSA backing from Williams to Lotus, Venezuelan Maldonado initially found an unreliable and uncompetitive E22 car, but he has also struggled to keep up with Grosjean while being involved in multiple on-track incidents.
But Lopez backed Maldonado to eventually get it right.
"We've lived the same thing with Romain, and people wrote him off, but now we've got people knocking on our door to see if he can be in their team," said Lopez.
He is referring to Frenchman Grosjean's struggles in 2012, when he was written off as a "nutcase" by Mark Webber and even banned for a race by the FIA.
But Lopez says Grosjean, 28, is now a sought-after driver in the F1 paddock.
"His drives last year meant there were a couple of teams knocking on the door to find out what he was doing, and now we've the same this year," he said.
"We don't have the budget of some of the other teams, so there is a point up until which we will fight," he said.
"But Romain is really happy here, he is part of the family, and I don't think he is planning on going anywhere."