Is the money market model based on assumption of no interest rate targeting on the part of the central bank? This is quote from Gregory Mankiw's macroeconomics text about mechanism of formation of the interest rate in the money market model:

How does the interest rate get to this equilibrium of money supply and
money demand? The adjustment occurs because whenever the money market is
not in equilibrium, people try to adjust their portfolios of assets and, in the
process, alter the interest rate. For instance, if the interest rate is above the equi-
librium level, the quantity of real money balances supplied exceeds the quantity
demanded. Individuals holding the excess supply of money try to convert some
of their non-interest-bearing money into interest-bearing bank deposits or
bonds. Banks and bond issuers, who prefer to pay lower interest rates, respond to
this excess supply of money by lowering the interest rates they offer. Conversely,
if the interest rate is below the equilibrium level, so that the quantity of money
demanded exceeds the quantity supplied, individuals try to obtain money by sell-
ing bonds or making bank withdrawals.To attract now-scarcer funds, banks and
bond issuers respond by increasing the interest rates they offer. Eventually, the interest rate reaches the equilibrium level, at which people are content with their
portfolios of monetary and nonmonetary assets.

I also noticed that the money supply curve is strictly vertical.
Both of these things make me suspect that this model assumes that the central bank doesn't target the interest rate. Am I right? Or is it somehow possible for the central bank to target the interest rate in this model without breaking the interest-rate forming mechanism outlined above?
I remember making myself the same question when studying those models in Mankiw's book. The answer I arrived is that from the point of view of the model, the Central Bank's policy is reflected in the money supply variable, and the interest rate variable is an abstraction that represents the main interests rates in an economy that are given by the equilibrium.
Think about this, in the model when there's an increase in money supply, what happens with the equilibrium interest rate ceteris paribus? It goes down. And the opposite is also true. But, who controls the money supply variable? The Central Bank.
So if you look at what happens in reality is somehow like that, the Central Bank cuts rates so the money supply decreases. Obviously the mechanism by which this happens in reality is different compared to the model, even they're like the 'opposite', but remember that models simplify reality in order for it to be more understandable, and in this case the CB intervention is modeled this way.