Prime Minister Ariel Sharon was scheduled to meet his cabinet on Sunday where Justice Minister Tommy Lapid, head of the centre-right Shinui party, was to present the new route, Israeli radio said.
Such a plan would save an estimated $500 million, the radio added.
The proposed route would enable Israel to better fight its case at the International Court of Justice (ICJ) in The Hague when the matter is heard on 23 February.
"Legal experts in Israel have come to the conclusion that it is necessary to modify the route of the barrier in certain problematic areas, with the aim of sparing the Palestinians from suffering," a senior official from Sharon's office told Israeli daily Yediot Ahronot.
Sharon's bureau chief Dov Weisglass will travel to Washington soon to meet US Secretary of State Colin Powell and National Security Adviser Condoleezza Rice, when he is expected to discuss issues relating to the barrier, the paper added.
"Legal experts in Israel have come to the conclusion that it is necessary to modify the route of the barrier in certain problematic areas, with the aim of sparing the Palestinians from suffering"
Following an Arab-backed resolution, the United Nations General Assembly has asked the ICJ to rule on the legality of the barrier.
Although the court can give an advisory opinion, it has no legally binding effect.
The barrier, which is now being referred to by the prime minister's office as "the anti-terror fence", is to stretch 730km in its present form.
Israel claims that the barrier, which in some areas cuts deep into the West bank, is vital for its security, but the Palestinians say it is a landgrab and an attempt to pre-empt the borders of a future Palestinian state.
Before the world court hearing, judges from Israel's High Court will also debate the legality of the barrier in what is considered a dress rehearsal for the ICJ ruling.
Gaza closure lifted
The Israeli army has lifted the closure of the Gaza Strip it had imposed on Wednesday after a bombing at the Erez crossing point, a military spokesman said.
"The closure has been lifted and the Palestinian workers in the Gaza Strip are authorised to use the Erez crossing terminal," he said.
The industrial zone next to the terminal was also reopened, he added.
About 5000 Palestinians pass through the Erez checkpoint daily to work in Israel.
Israeli military sources had said on Friday the crossing would remain closed until repairs had been carried out and more effective security measures put in place.