I cannot find anything close to what you have quoted in any of the rules I have looked at online.
However, the general rule is: Whenever you would owe money, you have the opportunity to do trading with other players to raise the funds, including with the person who you owe money to, but they are not obliged to accept.
This site backs this up and claims it is from official tournament rules.
If you do not have enough cash to cover rent, you may sell any other
asset you have in the game, such as unimproved properties to raise the
rent. You can sell the properties for whatever amount the market will
You may also make a trade of unimproved properties (or properties and
cash) to the landlord, which is effectively selling the properties to
that person for the amount in question.
The only time a sale cannot take place is if a player will be cheated.
For example, Player A lands on Boardwalk with hotels and owes $2,000
to Player B. Player A cannot raise enough cash or make a trade with
Player B, so he is effectively bankrupt and should turn over all
assets. Player A would not be able to make a deal with Player C to
sell some properties for less than their value (say the red properties
for $1) since that would cheat Player B. He could sell them for more
than their purchase value, however.
There is a lot of flexibility in how you can finance your debts. Most
limitations are that the deal is limited to the game (you can’t trade
a cookie or a kiss) and that you don’t cheat the player due money by
making a deal with another player when owing money. Other limitations
involve the inability to grant immunity to someone. It’s simply not
Further, from the official rules on the Deluxe edition of Monopoly has this to say and supports the general rule I mention above:
Using a Mortgaged Property to pay a debt: If you owe money to any of your opponents, you can offer them a piece of mortgaged property to
cover all or part of your debt. Your opponent has the option of
deciding whether or not to accept it. If you opponent accepts, he/she
must immediately pay 10% of the mortgaged value.