For an excellent article on it please read here, for those who want the cliff notes continue reading.
The short answer is yes. The long answer continues as follows: The issues are thus; size of the whale, the esophagus, and surviving in the stomach acid.
The whale had to be a sperm whale which is 90,000 pounds and 52ft in length! They have been seen in the Mediterranean Sea (Jonah’s route) and are large enough to swallow a man. The issues is the esophagus which would be tight and hard for a whale to swallow an average man, but if Jonah was a wee-little lad, it could be possible! Once in the stomach there would be plenty of room but the acid would tarnish the skin and the lack of oxygen would likely cause a person to pass out. Obviously, Jonah’s prayer was recorded outside of the whale though it is clear why he wrote, “My soul fainted within me” (Jon. 2:7, KJV).
Some Christians claim it was a fish as the Hebrew is clearly a fish. Point taken. However, Jesus said it was a sea monster. “For just as Jonah was three days and three nights in the belly of the sea monster” (Matt. 12:40, NRSV). The Greek for sea monster is kētos which in latin is cetus and is where we get cetology (study of whales). It’s a bit circular but the ancients weren’t idiots who made up fantasy like George Lucas. They based words from empirical data. They saw a great giant sea creature (whale) and gave it a word!
Now, does it really matter what swallowed Jonah? If Jonah’s message was dependent on a whale (i.e. Veggietales, “He has the smell of the great fish!”) then why not add more to the story? The Jews see Jonah as the text for Yom Kippur or the Day of Atonement. It seems the historic parable is about compassion, mission, repentance. YHWH ends the books with, “And should not I pity Nineveh, that great city, in which there are more than 120,000 persons who do not know their right hand from their left, and also much cattle?” (Jon. 4:11, ESV). It’s a tale to love our neighbor, to help an enemy.
“For the Lord your God is God of gods and Lord of lords, the great, mighty, and awesome God who is unbiased and takes no bribe, who justly treats the orphan and widow, and who loves resident foreigners, giving them food and clothing. So you must love the resident foreigner because you were foreigners in the land of Egypt. Revere the Lord your God, serve him, be loyal to him, and take oaths only in his name” (Deut. 10:17-20, NET Bible, italics added).
Hope this article helps and to God be the glory!