Can I conduct an auction to sell my property?
From the rules:

SELLING PROPERTY...Unimproved properties, railroads and utilities (but
not buildings) may be sold to any player as a private transaction for
any amount the owner can get; however, no property can be sold to
another player if buildings are standing on any properties of that
color-group. Any buildings so located must be sold back to the Bank
before the owner can sell any property of that color-group. Houses and
hotels may be sold back to the Bank at any time for one-half the price
paid for them. All houses on one color-group must be sold one by one,
evenly, in reverse of the manner in which they were erected. All hotels
on one color-group may be sold at once, or they may be sold one house
at a time (one hotel equals five houses), evenly, in reverse of the
manner in which they were erected.

You can see that it can be sold to any player as a private transaction. There is nothing in the rules that forbid an auction.