The Spain international sustained a serious knee injury in Bayern's 2-0 Supercup loss against Borussia Dortmund and will consequently be out of action for at least the remainder of 2014.
Guardiola admitted at the weekend that he would like to sign a replacement for Martinez, with Roma star Mehdi Benatia allegedly topping the former Barcelona coach's wishlist.
However, the Morocco international's hefty pricetag could prove to be too much of an obstacle and Guardiola has made it clear that he is happy to work with his current squad if no fresh blood comes in.
"It would be great if something's possible on the transfer market," Guardiola was quoted as saying by Bild.
"But if it's not possible, so be it. We will just keep working with the players we already have.
"It's not a problem for me."
With Holger Badstuber, Dante and Jerome Boateng, Bayern have just three fit accomplished centre-backs in their squad following Martinez's absence.