The Millennium Falcon was so easy to track that Han Solo found it almost as soon as it left the planet Jakku. He later took Rey and Finn to Maz Kanata to find a ship for them to take to the Resistance, since the Millennium Falcon was traceable. However at the end of the movie they use the ship to go to the super secret location of Luke Skywalker.
The ship was found near Jakku because of a homing beacon. Han didn't want to face Leia and may have made up the "clean ship" rationale. Also, there are no First Order ships or installations in the region where Luke is hiding.
While hauling rathtars in their large cargo ship, Han and Chewie happened to be in the vicinity of Jakku, a world they had searched before for the Falcon since Han knew that the smuggler who had stolen it (an individual by the name of "Ducain") had operations on Jakku.
They happened to be passing near Jakku at roughly the same time that Rey and Finn had used to Falcon to escape the planet. When the Falcon was activated, its homing beacon (a feature known to Han and Chewie) had also been activated.
It was this homing beacon that let Han know where the Millennium Falcon was and why they intercepted it.
In the novelization, Han tells Chewie,
As Han and Chewie were well aware of this beacon, Chewie would almost certainly have disabled it before they made the trip to Luke's planet.
It's true that a confusing bit of dialogue occurs in the cantina. When Finn asks why they are there, Han responds with
However, Han's statement may have been intentionally deceptive. The First Order may not have been tracking the ship (and if they were trying to, it wasn't effective — it was actually a First Order collaborator at the cantina who tipped off the Order). The truth seems to be that Han doesn't want to take them to the Resistance because he doesn't want to face Leia. Maz Kanata essentially confirms this when she tells Han that he's been running from his troubles for too long.
Another thing to note is that, whether or not the Falcon can be tracked by the First Order, once the Falcon makes the jump to hyperspace from the Resistance base to a sector near Luke, the Falcon will be in territory that is unoccupied and uncharted by the First Order. In other words, there will be no First Order ships near enough to do any tracking. To exploit the Falcon to find Luke, a First Order ship would have to piggyback the Falcon's hyperspace jump and then track it in normal space to Luke's hideout.
To echo Admiral Piett's frustrated hyperbole from Empire Strikes Back,