Abidal came on as substitute and was handed the armband for Claudio Ranieri's men in the final 35 minutes of their 3-2 defeat to Fortuna Dusseldorf on Sunday.
And the experienced 33-year-old, who played at Barcelona for six seasons, says he would relish the extra responsibility of leading his newly promoted Ligue 1 side.
“During my career, I’ve never tried to be captain. But I’ve changed," he told L'Equipe.
“I have more experience and the coach wants to trust me. I speak Spanish and I want to help young people. If it means becoming captain, I will accept and take on the job without any problems.
“We have not yet spoken. I'm not against it; on the contrary, if the coach has confidence in me, I will make him feel it. This is very important; I think I can bear it. Now, only time will tell.”
Claudio Ranieri has already hinted at who may skipper the side, with Abidal being one of three candidates.
"I’m considering between last year's captain [Valere] Germain, [Jeremy] Toulalan or Abidal," former Chelsea boss Ranieri told reporters. "Abidal is coming from the Monaco academy."
Abidal spent two seasons with Monaco earlier on in his career from 2000 to 2002.