The club has been involved in discussions with West Bromwich Albion over Rondon for some time.
Up to now, United have been unwilling to meet his £16.5million release clause.
A loan swap deal involving Gayle – who was an unused substitute for Saturday’s goalless draw against Porto at the Estadio do Dragao – has been mooted.
Newcastle manager Rafa Benitez was asked about incoming signings after the club accepted a £20million bid from Fulham for Aleksandar Mitrovic.
“We are working, trying to bring new players to bring new competition, but still there’s no news,” said Benitez, who has lost defender Florian Lejeune to a long-term injury.
Benitez was coy about Gayle’s future after leaving him on the bench.
Asked about speculation over his future, he said: “It’s a time for rumours, so we just have to keep doing our job. Hopefully, we can do what we have to do to improve the team.”
Mitrovic’s move to Fulham should be confirmed in the next 24 hours.
Meanwhile, Lejeune is facing a lengthy lay-off after suffering a cruciate ligament injury.
“I think it’s a cruciate ligament,” said Benitez. “He will need an operation. We need to decide exactly when, but I think we will lose him for a while.”
Lejeune posted a message to fans on Twitter pledging to be back “as quickly as possible”. The 27-year-old tweeted: “During my last training session, I left the field due to an injury,” said the 27-year-old.
“After further medical examination, the doctor told me I have a cruciate ligament injury.
“I’ll have surgery in the next few days. I’ll do everything I can to get back as quickly as possible on St James’ Park.”
Benitez – whose side play Braga on Wednesday night – is looking to sign another defender before the August 9 transfer deadline.