[5] Ruth Gledhill, the religious affairs correspondent of The Times, mentioned him as a possible candidate for the position of Archbishop of Westminster in succession to Cardinal Cormac Murphy-O'Connor.

[8][9] In 2015, a comprehensive agreement was signed by the Holy See and Palestine which may serve the twofold goal of stimulating peace in the Middle East and providing a model for similar treaties.

Gallagher voiced hope “that the present agreement may in some way be a stimulus to bringing a definitive end to the long-standing Israeli-Palestinian conflict, which continues to cause suffering for both parties.

I also hope that the much desired two-state solution may become a reality as soon as possible.”[10] In July 2015, Gallagher said in an interview that the Joint Comprehensive Plan of Action (the 2015 Iran nuclear deal) was viewed "in a positive light" by the Holy See because it believed that controversies and difficulties must always be resolved through dialogue and negotiation.

[11] In a February 2016 interview he said, "Let's not be kidding ourselves about what the stakes are here: If we are going to bring peace, if we are going to reconcile nations, if we are going to secure countries and communities, particularly minorities, particularly people who are persecuted, we are going to have to make an unprecedented effort," Gallagher speaking specifically of the crisis in Syria and Iraq, where so-called Islamic State militants have captured large swaths of territory and driven out tens of thousands of Christians and members of other minority groups, Gallagher said he is hopeful for a resolution of the conflict".

He also met with the Catholic Bishops' Conference of the Philippines in Malaybalay in Bukidnon.”[20] Gallagher speaks native English, near-native Italian and fluent French and Spanish.