Christian Solidarity Worldwide says there is no law to defend people who are switching from another faith to Christianity.
Several politicians are calling for conversion from one faith to another to be banned.
Martin Gore, from Christian Solidarity Worldwide, told Premier: "It's very uncertain that...[religious freedom] will be guaranteed in the new constitution.
"International treaties that Nepal has signed actually say that everyone must have the right to adopt a religion of their own choice, and the clauses [of the constitution] we've seen so far did not guarantee that.
"They have got proposals put before their Constituent Assembly some years ago that banned all conversions in the new penal code. Now that hasn't been considered on the floor of the House, but those proposals are there.
Out of a population of almost 30 million, just 2.85% in Nepal are Christians.
The country became a secular state after a decade-long civil war between 1996 and 2006. As part of the ceasefire, it was required to create a constitution, which has still not been made eight years later.
A draft constitution is due to be released in January, with consultations and redrafts to take place throughout 2015.
Hear more from Martin Gore: