Clubs from Germany, Scotland and Spain have already launched fund-raising initiatives, with Bundesliga giants Bayern Munich notably announcing a donation of one million euros ($1.1m).
Roma, the Serie A runners-up for the past two seasons, have labelled their initiative "Football Cares" and on Tuesday club president James Pallotta will kick things off by making a "large donation", according to the league's official website, www.legaseriea.it.
A statement by Roma said: "Football has the power to reach millions and by uniting for 'Football Cares', we can make a real difference no matter how small an individual donation is."
Fans can make a donation to the cause on the JustGiving platform. Roma said all money raised will go to the United Nations Refugee Agency, Save The Children, International Rescue Committee and the Red Cross.
United Nations (UN) estimates put the number of people being driven out of their homes by persecution and war at 60 million.
Germany's Bundesliga clubs have been particularly proactive in launching initiatives.
Bayern are working with Munich authorities to set up 'training camps' for children to receive German lessons, meals and football kits.
For their next home match against Augsburg on September 12, Bayern players will walk out hand-in-hand with both a German and a refugee child as a mark of support for the integration of refugees.
"We at FC Bayern consider it our socio-political responsibility to help displaced and needy children, women and men, by supporting and assisting them in Germany," Bayern's chairman Karl-Heinz Rummenigge wrote on the club's website.