Guardiola believes ‘anything can happen’ with Mbappe and is refusing to rule out a sensational move to the Etihad.
Real remain firm favourites to sign the teenager after tabling a world record £160million bid and offering Mbappe a six-year contract at the Bernabeu worth £270,000-a-week before tax.
But Guardiola pointed out that City’s backing from Abu Dhabi has put them on the same financial footing as the Spanish giants.
‘Madrid doesn’t have more than Manchester City have,’ he said before his City side trounced Real Madrid in Los Angeles in the early hours of Thursday, UK time.
‘Players are very important and we always try to get the best players possible.
‘Abu Dhabi came in and invested in the team. Over the past five or six years we climbed to the top and we’re now in the top three or four. In order to get to the level of Madrid or Barcelona we just need time.
‘The Premier League is so attractive and the agreements are good. All the clubs think about their potential and their squads getting better. We try and we will see.
‘Now there is a period where there are a lot of doubts in terms of the players who will be here or not. We have to wait and meanwhile prepare the team as well as possible.’
City have held talks with Monaco over Mbappe having already signed Bernardo Silva and Benjamin Mendy for a total of £95m from the Ligue 1 club this summer.
But Guardiola made no attempt to hide his interest in the 18-year-old France striker when he was asked about the possibility of hijacking his move to the Bernabeu.
‘The player is still at Monaco, still on that team,’ he said. ‘Anything can happen. We are still looking at other players in the market. There are a lot of other players, but he is still on that team.
‘We have two exceptional forwards in Gabriel (Jesus) and Sergio (Aguero). The market finishes on August 31. We will see what happens.’
City have already paid out more than £200m for new players this summer – a record for a single transfer window – and signing Mbappe would push their spending above the £350m mark.
But Guardiola defended City’s outlay and admitted that the figures will continue to rise as Europe’s top clubs compete for the best players.
He added: ‘I could not imagine two or three years ago that people would pay £100m or £120m for one player. Now it’s happened and it’s going to happen more. I would like to pay less for the club, but the market is the market.
‘We had four full-backs and Manchester City didn’t invest in a fullback for the last seven years. All four were 31 or 32, and we decided we had to make the squad younger.
‘All the clubs spent a lot of money not just us. We are going to see until August 31 the amount of new transfers coming. We will see £70m, £80m, £90m, £100m, maybe more than that. Maybe one day it’s going to stop, we will see.’