According to “Reception of Baptized Christians into the Full Communion of the Catholic Church”, n. 9 (also known as RCIA #482, using the USA numbering):
“If the profession of faith and reception take place within Mass, the candidate, according to his or her own conscience, should make a confession of sins beforehand, first informing the confessor that he or she is about to be received into full communion. Any confessor who is lawfully approved may hear the candidates’ confession.”
(From The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 277).
The general rule for non-catholic Christians is in the Code of Canon Law, canon 844:
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
§5. For the cases mentioned in §§2, 3, and 4, the diocesan bishop or conference of bishops is not to issue general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community."
(From vatican.va/archive/ENG1104/_INDEX.HTM ).
If the above cases are considered not to apply, another approach would be to have the Rite of Reception earlier. This could be discussed with the priest, along the lines of “The rite is so arranged that no greater burden than necessary (see Acts 15:28) is required for the establishment of communion and unity.” (RCIA #473, USA numbering). A delay in reception means a burden, because of the difficulty of me receiving the sacrament of reconciliation.