The Royal College of Nursing could be willing to accept a 10% pay rise, with the union's leader calling on the Government to meet it "halfway".
The general secretary of the Royal College for Nursing (RCN), Pat Cullen, has previously said the union's demand for a 19% rise, dismissed by the Government as "unaffordable", is simply a "starting point", and that she would put any new offer to her members.
The PA news agency understands the union could be willing to accept a pay rise of about 10%.
In an interview with Times Radio's Past Imperfect podcast, reported by The Times, Ms Cullen said: "There is a rhetoric out there that says the Royal College of Nursing is unrealistic, it's looking for something that's totally unachievable, it's looking for 19%.
"Now, I could sit here all day and tell you nurses' pay has dropped by 20% over the last decade.
"Do I believe those nurses are entitled (to 19%)?
"Absolutely, I believe they're entitled to 19%.
"But we also understand the economic climate that we're working in.
"And what I would say to (Health Secretary) Steve Barclay and to the Prime Minister is get into a room and meet me halfway here and do the decent thing for these nurses."
More Strike Action
Thousands of nurses walked out on December 15 and 20, and the RCN has said its members will strike again on January 18 and 19 unless negotiations are opened.
The planned action would take place at more NHS employers in England than the previous strikes, increasing from 44 to 55 trusts, according to the RCN.
The union has also warned that strike action could continue over the next six months unless an agreement can be reached.
A Department of Health and Social Care spokesperson said: "The Health and Social Care Secretary wants to have an honest conversation with the RCN about what is affordable in pay settlements for next year during these challenging times, and is keen to meet for discussions as soon as possible.
"We have accepted the recommendations of the independent NHS Pay Review Body in full and have given over one million NHS workers a pay rise of at least £1,400 this year. This is on top of a 3% pay increase last year when public sector pay was frozen and wider Government support with the cost of living."
– Past Imperfect's interview with Ms Cullen is due to be played on Times Radio at 9pm on Sunday and to be released as a podcast on Friday.
This article contains information from PA Media.