"The minister hopes to see Marvan in the next few days to hear his side of the story. He is keen to see an end to the present row between him and the selectors," spokesman Kapila Bamunuarachchi told AFP.
Sri Lanka Cricket (SLC) have already named their squad for the two Test matches in Australia, but the sports minister's approval is needed to make it official.
Atapattu was not immediately available for comment.
Lokuge on Tuesday met the selection panel, including chairman Asantha de Mel, to iron out the problems.
SLC sources said the minister wanted De Mel to amicably settle the issue with the former captain.
Atapattu had earlier lashed out at the selectors, saying he had no faith in them although he planned to play for at least two more years.
De Mel said last week he had hoped to meet Atapattu to sort out any differences, but the former captain said he was not keen to see the officials.
A similar intervention by Lokuge over the early retirement of leg-spinner Upul Chandana yielded no results despite expectations that the bowler would be convinced to make himself available for selection.