The correct thing is to consume the host immediately on receiving it. This can be a challenge, which may require careful planning, since singing is encouraged while Communion is distributed.
From the 2002 General Introduction to the Roman Missal (GIRM) which can be accessed from
romanrite.com/girm.html :
“161. If Communion is given only under the species of bread, the priest raises the host slightly and shows it to each, saying, Corpus Christi (The Body of Christ). The communicant replies, Amen, and receives the Sacrament either on the tongue or, where this is allowed and if the communicant so chooses, in the hand. As soon as the communicant receives the host, he or she consumes it entirely.”
About the singing:
"86. While the priest is receiving the Sacrament, the Communion chant is begun. Its purpose is to express the communicants’ union in spirit by means of the unity of their voices, to show joy of heart, and to highlight more clearly the “communitarian” nature of the procession to receive Communion. The singing is continued for as long as the Sacrament is being administered to the faithful.
[Footnote 74:Cf. Sacred Congregation for the Sacraments and Divine Worship, Instruction Inaestimabile donum, 3 April 1980, no. 17: AAS 72 (1980), p. 338. ] If, however, there is to be a hymn after Communion, the Communion chant should be ended in a timely manner.
“Care should be taken that singers, too, can receive Communion with ease.”