The Bafana Bafana duo attracted foreign interest after the recent World Cup, but there is no deal on the table yet.
Sundowns have, however, turned down a R7m offer for Mphela from Russian club, Terek Grozny, while Gaxa could have moved to Belgium to join Lierse SK had the Brazilians accepted a R4m offer right after the global showpiece.
Lopez, though, is hoping 'Killer' and 'Pa' will don the Sundowns colours once again.
"I hope they will stay with the team," he told Football365.co.za.
"The whole technical team wants them to stay, because they are very good players for us. They are international players and they are respected by their team-mates and that is very important," he said.
"They are Sundowns players and we will play them in the match against Ajax Cape Town on Friday," Lopez said.
Hristo Stoichkov's former assistant indicated after the recent Telkom Charity Cup that he was searching for another striker, but now says it depends on whether Mphela stays.
"If he stays with the team we are not going to buy another striker. I'm happy with my team at the moment, but if Mphela goes overseas then I'm going to buy a striker to replace him. If he stays, there will be no need to buy another striker, because we are strong upfront," he said.
"It will be good for Mphela to play overseas and it will be good for Mamelodi Sundowns, because maybe they will get a good offer for the player," he added.
Meanwhile, Lopez expects his players to win the MTN8 quarter-final clash against the Urban Warriors at Athlone stadium.
"I want consistency with the team. We must win and keep on winning, that's what the club boss wants.
"We know Ajax from last season, but things have changed now. We will see, but of course we want to win. We respect Ajax, but we must win," Lopez concluded.