Gianni came up with the assurance at a meeting with Prime Minister Sheikh Hasina at her office.
PM's Press Secretary Ihsanul Karim briefed reporters after the meeting.
The FIFA president said he is happy seeing the performance and improvement of Bangladesh football.
He suggested the Bangladesh Football Federation (BFF) to maintain contact with FIFA regularly.
The Prime Minister said her government is constructing 492 mini-stadiums at sub-district levels across the country for the promotion of games and sports.
She said primary school-level sports competitions are arranged for both boys and girls in Bangladesh so that more and more children become interested in games and sports.
The Prime Minister said her family members were involved in sports and games and her brother Sheikh Kamal was the founder of sports club Abahani Krira Chakra.
PM's Private Industry and Investment Adviser and Chairman of Abahani Limited Salman F Rahman, State Minister for Youths and Sports Zahid Ahsan Russell, BFF President Kazi Md Salahuddin, BFF Senior Vice President Abdus Salam Murshedy MP and its Vice President Kazi Nabil Ahmed were present on the occasion.
Gianni Infantino, leading a five-member FIFA delegation, arrived in Dhaka in early hours of Thursday on a day-long visit responding to an invitation of the BFF.
Infantino is the third FIFA President to visit Bangladesh after Sepp Blatter and Joao Havelange.
Earlier, Italian Air Force chief Lieutenant General Alberto Rosso met Prime Minister Sheikh Hasina her office.
During the meeting, Alberto Rosso offered training to Bangladesh Air Force personnel in Italy.
In reply, the Prime Minister urged the Italian Air chief to arrange training in Italy for Bangladesh’s Air Force personnel over fighter helicopters and transport planes.
PM’s Principal Secretary Md Nojibur Rahman, Principal Staff Officer of the Armed Forces Division Lieutenant General Md Mahfuzur Rahman, PMO Secretary Sajjadul Hassan and Italian Ambassador to Bangladesh Enrico Nunziata were present.
On Wednesday, the Chief of the Air staff of Italian Air Force along with three delegation members arrived here on a three-day official visit to Bangladesh.
Alberto Rosso called on Chief of Air Staff of Bangladesh Air Force (BAF), Air Chief Marshal Masihuzzaman Serniabat at the Air Headquarters on the same day.