No. There's nothing in the film/s that specifically indicate why Han came back other than the exchange that occurs shortly after.
LUKE: I knew you'd come back! I just knew it!
HAN: Well, I wasn't gonna let you get all the credit and take all the
Luke and Han look at one another, as Solo playfully shoves at Luke's
face. Leia moves in between them.
LEIA: (laughing): Hey, I knew there was more to you than money.
We're just left to assume that he changed his mind after having left his friend to fight the Death Star on his own, possibly with the encouragement of Chewbacca who we now know was a decorated war hero and long-time supporter of the Jedi.
For a better explanation we need to turn to other sources. The new Junior Novelisation adds a little bit of additional speech.
Han shrugged. “Well, I wasn’t gonna let you have all the credit!”
Chewbacca growled behind Han, giving the captain a little shake.
“All right, all right, and because we wanted to make sure you got out of this mess in one piece!” Han said. “How does it feel to be a hero?”
A New Hope: The Princess, the Scoundrel, and the Farm Boy
As does the original trilogy novelisation written by
Alan Dean Foster George Lucas
“I knew you’d come back,” Luke was shouting, “I just knew it! I
would’ve been nothing but dust if you hadn’t sailed in like that,
Solo had lost none of his smug self-assurance. “Well, I couldn’t very
well let a flying farm boy go up against that station all by himself.
Besides, I was beginning to realize what could happen, and I felt
terrible about it, Luke—leaving you to maybe take all the credit and
get all the reward.”
Star Wars: Official Novelisation
The official databank article on Wookiees gives us this snippet
Chewie helped convince Han to intervene at the Battle of Yavin
And in a novel set shortly after the Death Star's destruction, Chewie and Han have a brief discussion about his reasons for returning. Han confirms that his primary reason for coming back was his desire to help Luke. Chewie seems to be of the opinion that it was also about his desire for a financial reward.
“Name one time. Name one.”
The Wookiee rumbled and began speaking. After thirty seconds or so, Solo cut him off.
“You’ve made your point.”
“We came back to help the kid.”
“That was not all about a reward.”
Smuggler's Run: A Han Solo & Chewbacca Adventure