Trump and Putin are to attend celebrations of the centenary of the armistice that ended World War I on 11 November in France.
Macron discussed organising a Trump-Putin meeting in a phone calls on Saturday, according to the RIA news agency.
Separately Kremlin spokesman Dmitri Peskov announced that the phone call had taken place in the run-up to the Istanbul summit.
The French presidential palace said that Macron reiterated his objectives to "extend the ceasefire in Idlib, prohibit chemical weapons, ensure access to humanitarian aid and find a timetable for the political process".
The summit opened during the afternoon with Macron, Putin, Turkish President Recep Tayyip Erdogan and German Chancellor Angela Merkel attending.
It was to discuss the situation in Idlib, the last rebel-held bastion, and a possible political solution to a conflict that has cost at least 400,000 lives over the last seven years.
A key task of the summit would be to call for a commission to draw up a new constitution for Syria, Turkish presidential spokesman Ibrahim Kalin said on Friday.
France wanted it to be made up of a third representatives of President Bashar al-Assad's government, a third opposition groups and a third independent figures, with the aim of organising a meeting by the end of the year.
A new constitution would pave the way for new elections.
Russia, which backs the Assad regime, wanted to discuss the return of refugees and reconstruction of Syria's infrastructure.
On Friday rebel groups, which have previously termed Moscow's intervention an "occupation", indicated they were ready to talk to Moscow's representatives.
The peace process has stalled, a fact underlined by the resignation of UN envoy Staffan de Mistura, which takes effect next month.
His two predecesors, Lakhdar Brahimi and Koffi Annan, also resigned, complaining that their efforts were leading nowhere.