The Greek verb translated asked is the same verb and tense rendered begged in verse 40, and it may best be taken with that meaning here (see the New English Bible).

To go to Capernaum is literally “that he might come down.” The verb “to come down” is the same one used in 2.12. In 2.13 the special term for a journey to Jerusalem is used (literally “to go up”). Good News Translation makes explicit the place to which Jesus was asked to come, namely, Capernaum.

In some languages the request the government official makes to Jesus is best put into direct discourse, for example, “begged him, ‘Come to Capernaum and heal my son, who is about to die.’ ”

Who was about to die is translated by Jerusalem Bible “as he was at the point of death.” In some languages the more appropriate way of saying about to die may be “is now dying” or “is in the process of dying.” In some languages one may even say “is half dead” or “is now leaving life.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on the Gospel of John. (UBS Handbook Series). New York: UBS, 1980. For this and other handbooks for translators see here .