Johannesburg-born Conway made his Test debut against England at Lord's last year and has been in sensational form since, with three tons and two 50s in his nine innings to date. That includes a double century on debut.
Many of the touring South Africans have played with and against Conway in the country's domestic cricket, so are well aware of his qualities.
"He is playing with a different badge on his chest now and has had a great start to Test cricket. His numbers speak volumes and he is in a massive purple-patch," Elgar told reporters on Thursday.
"But we don't see him as a South African guy anymore, he is living here and playing for another country."
"I am sure there will be some friendly chats off the field because a lot of guys know him and played with him and against him. But once match-day comes and you walk over that white line, it is all business, irrespective if he is your friend or not."
The South Africans have begun to practice for a few hours each day having all returned negative COVID-19 results in the first three rounds of testing since their arrival in the country.
Elgar says they are thankful for the discussions between the respective cricket boards and New Zealand government to ease restrictions and "make life bearable".
"It is impossible to get guys to come and tour here if you are doing a straight 10 days where you can't leave your room, basically living in jail without the opportunity to go outside and get some fresh air, practice or gym," Elgar says.
"They have tried their utmost to make life bearable for us knowing that doing 10 days straight is absolutely not human for cricketers, let alone citizens.
"We do want to be here and play against New Zealand, no doubt, but you also have to meet the touring team halfway."
