A journalist from US broadcaster CBS who was travelling with him presented him with the bat belonging to White Sox legend Nellie Fox.
Leo has been a fan of the baseball club in his home city of Chicago since his youth.
The flight on Thursday morning travelled from Rome to Ankara at the start of the Pope's trip to the Middle East.
Other journalists travelling with him also gave the Pope gifts, such as pecan and pumpkin pies, which are popular in North America for Thanksgiving.
The gifts also included an icon of Our Lady of Guadalupe, who is venerated in Latin and North America.
New Synodal Conference: "We shall see"
Before the almost three-hour flight began, Leo XIV addressed a few words to the journalists from all over the world. "Happy Thanksgiving", he wished his fellow travellers from his home country, adding that there were many reasons to be thankful.
He thanked the media professionals for their service in spreading a message of harmony and unity, peace and brotherhood, which were at the centre of the trip.
He then went through the ranks and greeted each and every one of them individually. This also led to brief conversations.
When asked whether he would give his "OK" to the new synodal conference, in which bishops and laypeople in Germany are to consult and decide together in future, the Pope replied: "We shall see".