Peer, the women's world number 17, plans to compete in the WTA Qatar Open from February 18 to 24, which would make her the first Israeli to play a tour event in the Gulf region.
Erlich and Ram said they could follow suit by playing in the men's event in Dubai, from March 3 to 8.
"I don't think we have to involve anything in sport according to politics or religions."
Israeli tennis player
"That's one of our plans," Ram told reporters.
"We talked about it. We didn't decide 100 per cent yet. But definitely it's something new we want to do."
Peer told Reuters last week that she had been reassured by tournament officials in Qatar that she will be safe in Doha, and Ram said the ATP were working to give them the same assurances.
"I believe it's going to be safe for us," Ram said.
"The ATP will do all they can do to provide us the right security. All the top 20 players always play there, the best doubles teams.
"It's a big tournament to play. We want to play there. I heard it's a great country. I don't see a reason why not to go there and play."
Sport and politics don't mix
Ram said that Peer's decision to go to Doha had inspired them to consider playing in Dubai, despite the heightened tensions between Israel and its neighbouring Muslim countries.
"It's a great thing for tennis," Ram said.
"We don't have to involve, like everybody says, politics with sport. Arab country, Israelis... I don't think we have to involve anything in sport according to politics or religions."
The pair said they are currently exploring the possibility of getting a visa to enter the United Arab Emirates.
"And we are trying to keep it low profile right now, to see how it goes," Erlich said.
"We don't want really to (make) big news here or there before we really know what the situation is."
Ram said he and Erlich had received messages of congratulations from all over Israel, with even Ehud Olmert, the country's prime minister, getting in touch.