Romero is keen to leave Old Trafford after being omitted from the Premier League and Champions League squads by manager Ole Gunnar Solskjaer.
There is interest in the Argentina international at home and abroad ahead of a possible move in January but United are unlikely to make a decision until Henderson's immediate future is resolved.
After returning from a successful loan spell at Sheffield United in the summer, Henderson is content with his role at the club for now but has been told by England manager Gareth Southgate he will need to play more regularly if he hopes to challenge Everton's Jordan Pickford for the No.1 spot at the European Championships.
It opens up the possibility that Henderson, who has started three games this season, could be allowed to secure a loan move in January to boost his chances of ousting Pickford, who has come under fire for his performances at Goodison Park, before the tournament.
Henderson's temporary departure would increase Romero's chances of having to stay put until at least the summer when he could be a free agent.
The 33-year-old, valued at between £8 million and £10m by United, is under contract until the end of the season while the club also hold an option to extend his deal for another 12 months.
Solskjaer is keen to keep hold of an established No. 2 goalkeeper to provide cover for David De Gea during a season which could see his team play more than 60 games. His third choice is 37-year-old Lee Grant, who has made just two first team appearances in two-and-a-half years.
The 26-year-old has been struggling with a back injury which meant he was an unused substitute for the 2-1 Champions League defeat to Istanbul Basaksehir although he was able to return for the 3-1 win over Everton on Saturday.