Asked whether an accord could by struck by the end of August, Bach told AFP: "I am certainly hoping so because that would allow us to prepare well for the (IOC) session in Lima."
The double award at the IOC session in Lima is conditional on a prior agreement between the two cities and the IOC. If no agreement is reached, then the session will vote on 2024 only.
"We have already had informal talks between the parties at dinner yesterday (Tuesday)," following the IOC session earlier in the day which approved the double award, said Bach.
"Now we are going to talk to the two cities directly. I hope we can make reasonably quick progress. You have seen the reaction of both cities, it was very amiable. If that continues we can reach agreement soon."
French bid co-leader Tony Estanguet said the IOC would lead the talks and would draw up a new hosting contract that would include 2028 as part of the double-hosting award.
"Once we have that it will be easier to negotiate," he told AFP. "But at the same time we are not going to go back on the commitments that have been made by the Paris bid."
Paris has insisted that it is a candidate to host the 2024 Olympics only, while Los Angeles has indicated that it could be open to hosting 2028.
Delegations from the two cities -- led by French President Emmanuel Macron and LA Mayor Eric Garcetti -- were in Lausanne making fresh pitches to IOC voters on Tuesday.
Following the decision approving the double award deal, Garcetti and his Parisian counterpart Anne Hidalgo, voiced full confidence in the success of the upcoming talks.
"I now know that I am sitting up here with two mayors, from two cities that will host after Tokyo the next two Olympics," Garcetti said, referring to the 2020 Games in Japan.
Hidalgo assured that "the Games will return to Paris".
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)