WATCH MUTV club channel 24/7 via beIN SPORTS CONNECT | 2-week free trial
Incumbent owners, the Glazer family, tentatively put United up for sale in November and Ratcliffe was the first suitor to formally register an interest through his London-based chemicals company INEOS.
He was subsequently among the parties to submit initial bids ahead of a 'soft deadline' in February, with Ratcliffe and Qatari banker Sheikh Jassim bin Hamad Al Thani thought to be the two frontrunners.
While the exact value of the bids is unclear, the Glazers are reportedly looking for at least $7.2billion (£5.9billion) if they are to sell, which would be a new world-record fee for a sports team. The club was valued at $4.8billion (£4billion) by Forbes last year.
Recent reports suggested the bidders are increasingly confident the Glazers will approve a sale, with Ratcliffe and Sheikh Jassim expected to submit formal offers this week.
But Ratcliffe has given the clearest indication yet that he will not pay over the odds.
Speaking about the process to the Wall Street Journal, Ratcliffe said: "How do you decide the price of a painting? How do you decide the price of a house?
"It's not related to how much it cost to build or how much it cost to paint.
"What you don't want to do is pay stupid prices for things because then you regret it subsequently."
The second deadline for offers is apparently set for Wednesday, with Sky Sports claiming there could be as many as eight official bids.
Ratcliffe, a life-long United fan, was spotted at Old Trafford last Friday following a meeting with club officials.
Associates of Sheikh Jassim are said to have been in Manchester the day before, though he himself was not in attendance.