"We will work through the weekend to get a mandate for the offer that is on the table," said United Transport and Allied Trade Union (Utatu) general secretary Chris de Vos.
"I've got a smile on my face, it proves we are very positive."
De Vos's sentiments were not shared by fellow union, the SA Transport and Allied Workers' Union (Satawu).
"We are not going to recommend acceptance of the offer," said Satawu policy research officer Jane Barret.
Utatu and Satawu have threatened to strike from Monday if Transnet did not agree to increase its salary offer of eight percent.
Unions were demanding an increase of 15%.
Other issues included the use of temporary workers, maternity leave, medical aid contributions and housing allowances.
Trade unions had negotiated with Transnet late into Thursday night and De Vos said he believed his members may accept the latest offer.
Describing the situation as "sensitive", De Vos would not elaborate on Transnet's most recent offer
At a media briefing on Thursday, Transnet human resources executive Pradeep Maharaj said management's offer was now in "double-digits" but would require "trade-offs".
Barret confirmed that while Transnet had increased its wage offer, it had not satisfied Satawu's concerns about temporary workers and the other issues.
"The have increased the [wage] offer but have taken away other elements of the offer," she said.
"It doesn't make enough of a difference.
Barret said Satawu would take the offer back to its members for feedback but said it would be "surprising" if it was accepted.
"We anticipate the strike will continue on Monday," she said.
This raises the prospect of Satawu embarking on the strike without the support of Utatu.
"We would be very disappointed... it would be a great pity if we couldn't go out together," said Barret.
- Sapa