Rashford was in attendance at Madison Square Garden in New York on Monday night and was seen leaving the venue following an NBA match between New York Knicks and Brooklyn Nets.
The forward was pictured courtside with friends before he posed and signed shirts with NBA star Jalen Brunson during his trip while midfielder Casemiro flew to Orlando for a family holiday to Disney World, as seen on his Instagram.
Former Manchester United defender Neville has raised question marks over the choice of destination from the pair, and highlighted jet lag as a factor.
On the latest episode of the Stick to Football podcast, he said: “The professionalism, looking after your body and making sure you’re best prepared for the next training session is critical to every decision you make during the season.
“He [Marcus Rashford] has got a mental break, he’s got to get away and has got to rest with friends – then you talk about the choice of venue, how far do you fly, what’s the time difference, is that going to give a jet lag issue, is that going to give a stiffness issue from being on a flight for 12 hours?
“This is on Casemiro more than Rashford but if I’m 30 years old and I’m looking after my body – and he’s won five Champions Leagues and is an unbelievable player, but if he was away with Brazil for 10 days, we would say he would struggle this weekend because he’s been away.
“They [Casemiro and Marcus Rashford] have chosen that international break. If you are talking about the minor details in being as professional as you can be and as prepared you can be for a training session on a Monday night, that isn’t the best choice of venue.
“I’m not that wound up about [Marcus] Rashford and Casemiro going over to the United States but what I’m asking is, if you’ve got a four-day break, Portland is a 12-hour flight and an eight-hour time difference, your jetlag is bad, and you feel a bit [rough].
“They went to Portland and I’m asking the question based on professionalism – you’re playing badly, the team are losing, you’re 13th in the league, and there is a new manager coming in – would you choose that trip as a break to recharge your batteries? That’s not a recharging trip. It’s not right that.”
Ruben Amorim took charge of his first Manchester United training session this week following his arrival as new head coach, with the club releasing a seven-minute video on Monday showing both him and the players at Carrington.
Amorim starts his reign as boss with a trip to Ipswich in the Premier League on Sunday.