There is not a definitive yes or no to this, but it seems as though the Bible does mention dinosaurs. In Job 40:15-24, there is a description of a fearsome creature.
Behold now, Behemoth, which I made as well as you. He eats grass like an ox. 16 Behold now, his strength in his loins, and his power in the muscles of his belly. 17 He bends his tail like a cedar. The sinews of his thighs are knit together. 18 His bones are tubes of bronze. His limbs are like bars of iron. 19 He is the first of the ways of God. Let his maker bring near his sword. 20 Surely the mountains bring him food and all the beasts of the field play there. 21 Under the lotus plants he lies down, in the covert of the reeds and the marsh. 22 The lotus plants cover him with shade. The willows of the brook surround him. 23 If a river rages, he is not alarmed. He is confident, though the Jordan rushes to his mouth. 24 Can anyone capture him when he is on watch, with barbs can anyone pierce his nose?
Some have said that this might be a hippopotamus or even an elephant. But, it speaks of the power and the muscles of his belly (v. 16) and that his tail is like a cedar tree, which is huge (v. 17). This would not support a hippopotamus or elephant explanation. A crocodile has also been considered, but it doesn't eat grass (v. 15). So, no one knows for sure what it is, but whatever it is, it's formidable. Could it be a dinosaur?
Likewise in Job 41 is a description of another animal. The entire chapter is too lengthy to reproduce, so I will post the highlights. Job 41:1-3, 7-10, 12-23, 25-33.
Can you draw out Leviathan with a fishhook? Or press down his tongue with a cord? 2 Can you put a rope in his nose? Or pierce his jaw with a hook? . . . 7 Can you fill his skin with harpoons, Or his head with fishing spears? 8 Lay your hand on him; remember the battle; you will not do it again! 9 Behold, your expectation is false; will you be laid low even at the sight of him? 10 No one is so fierce that he dares to arouse him . . . 12 I will not keep silence concerning his limbs, Or his mighty strength, or his orderly frame. 13 Who can strip off his outer armor? Who can come within his double mail? 14 Who can open the doors of his face? Around his teeth there is terror. 15 His strong scales are his pride, shut up as with a tight seal. 16 One is so near to another that no air can come between them. 17 They are joined one to another. They clasp each other and cannot be separated. 18 His sneezes flash forth light, and his eyes are like the eyelids of the morning. 19 Out of his mouth go burning torches. Sparks of fire leap forth. 20 Out of his nostrils smoke goes forth, as from a boiling pot and burning rushes. 21 His breath kindles coals, and a flame goes forth from his mouth. 22 In his neck lodges strength and dismay leaps before him. 23 The folds of his flesh are joined together, firm on him and immovable . . . 25 when he raises himself up, the mighty fear. Because of the crashing they are bewildered. 26 The sword that reaches him cannot avail, nor the spear, the dart, or the javelin. 27 He regards iron as straw, bronze as rotten wood. 28 The arrow cannot make him flee. Sling stones are turned into stubble for him. 29 Clubs are regarded as stubble. He laughs at the rattling of the javelin. 30 His underparts are like sharp potsherds. He spreads out like a threshing sledge on the mire. 31 He makes the depths boil like a pot. He makes the sea like a jar of ointment. 32 Behind him he makes a wake to shine. One would think the deep to be gray-haired. 33 Nothing on earth is like him, one made without fear. 34 He looks on everything that is high . . .
As you can see from the underlined verses, whatever this creature is, it's extremely large and powerful. I think it is interesting to note that verses 18 to 20 speak of fire coming out of its nostrils and mouth. Legends are often based upon actual events. Perhaps the legends of fire breathing dragons are actually based on this creature, whatever it is that existed so long ago.
So, does the Bible mention dinosaurs? Perhaps it does.