The Spain international has made 10 appearances this season but only two of those have been starts - one of which ended with Monreal netting the decisive penalty in the Capital One Cup victory at West Bromwich Albion.
Gibbs has made 10 starts and earned a call-up to the England squad for their last two World Cup qualifiers. Monreal has been impressed by Gibbs' form but he is ready to take his own chance when it comes.
"I think that there is a very good rivalry there," Monreal told Arsenal Player. "I think we are two very good players, we give 100 per cent for the team in the training sessions and in the games.
"In truth it is a tough moment for me because the manager is choosing Kieran over me, but to be honest he is playing very well. All of the games that he’s played in he has done well, the team is on a good run, and I don’t see things changing in the short-term.
"There is nothing I can do but to keep training, do the best I can so that when I do get the nod from the manager, I can take advantage of my chance and show him that he can count on me.
"It is tough, every player wants to play, their maximum goal is to play the games, and right now I can only watch - I should say suffer - from the bench. But I will wait for my chance, keep on working, and show the manager that I am not giving up.
"The moment that Kieran steps off the gas, I will be there to take advantage of the opportunity, and carry on in that way."
Having two top-class internationals fighting for one spot is exactly what Arsène Wenger wants and Monreal knows that competition is imperative for successful clubs.
"Yes of course, the higher the level and the more competition for places, the better it is," he said.
"Logically, to have two quality players for every position, the player in the better form will get to play, and that means that you cannot relax. You cannot give up because if you do, you will not play, and that is very beneficial for the team obviously."Copyright 2016 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source