Eriksson said: "Beating United in a single match, of course, is positive but beating them over the course of a season or on an international level, given their fame, will be really difficult.
"That's why United are where they are and why we are where we are. There's a massive way to go but I'm happy that he talks that way and, if he wants, let's give it a go. It's a realistic target if the resources are there.
"That was a huge scale of investment but Thaksin doesn't say that this season we should be competing with United and the others - he's talking about the future. He wants to put the money there. I'm happy that he's saying it because it means he has these ambitions."
While the likes of United and Chelsea offer their top stars in excess of £100,000 a week, City have a wage structure with a top level of around £45,000. To put that in context, United defender Wes Brown has just turned down a similar amount.
Eriksson added: "I'm quite sure the chairman knows how much other clubs are paying for star players. How long this will take, I don't know.
"It depends on many things. How good the players we have are and how much better they can become and it also depends on the level of players we take in the future because they must be the very top - the very top.
"I don't know how many years I will be here but I would like to be here to see Manchester City playing Champions League football and winning trophies because that's the mid-to-long- term target for the club."