The Magpies have been linked with a loan move for the England striker, who is attracting the attention of a number of clubs after a chequered season with Manchester United.
Rashford found his starts at club level limited last season, but remains one of the most exciting talents in the Premier League.
The 20-year-old – who netted against Costa Rica at Elland Road on Thursday night – is understood to be open to a loan move this summer if Man United boss Jose Mourinho decides he is surplus to requirements.
Everton and Leicester are also keeping tabs on the situation while Magpies manager Rafa Benitez, frustrated at an impasse in transfer and contract talks with the club’s hierarchy, is looking to strengthen his striking options this summer.
One forward who won’t be part of his plans, however, is Aleksandar Mitrovic.
Mitrovic has hit form since January, when he joined Fulham on loan.
And the striker – who spent the second half of last season on loan at Fulham – scored a hat-trick for Serbia in their final warm-up game against Bolivia in Austria at the weekend.
Newcastle will demand upwards of £20million for the 23-year-old, who has been on the fringes under Benitez, and will be hoping that a strong World Cup will see more suitors come forward.
Meanwhile, Newcastle have also been credited with an interest in Nottingham Forest youngster Ben Osborn.
The 23-year-old is one of a number of playmakers the club has scouted over the last six months.
Stoke City are also keen on the versatile player, who can operate in a number of positions.