Forward Schick is flying to the Italian capital and it is anticipated he will undergo a medical on Tuesday.
He is then expected to join Roma in a loan deal with an obligation to buy in a total package understood to be worth around €40 million.
The 21-year-old impressed in his first Serie A season after joining Samp from Sparta Prague ahead of the 2016-17 campaign, scoring 11 goals in 32 league appearances, just 14 of which were starts.
"I'm happy," Schick told reporters at the airport in Genoa prior to his flight to Rome on Monday.
"Yes, Roma is [the right team for me]."
Schick had a medical at Juventus in June, but his protracted move to the Serie A champions ultimately collapsed last month.
Prior to the transfer breaking down, Juve director and Schick's compatriot Pavel Nedved predicted he would become the next Zlatan Ibrahimovic due to his world-class potential.