Fernandes, 31, has less than 12 months remaining on his current deal, though the club holds the option of an additional year, and is already in talks over fresh terms that would make him Manchester United's highest-paid player.
"The players know Bruno is absolutely vital if they want to have success," a source told The Sun.
"They all want him to sign a new deal and think execs should make him feel loved and give him a contract which reflects how important he is. He should be the top earner because he is the most important player in the dressing room."
The playmaker currently earns £300,000 a week, level with Marcus Rashford as the club's joint-top earner, but new terms are expected to push his salary above that mark. Fernandes turned down interest from the Saudi Pro League over the summer and has more recently been linked with a lucrative offer from Galatasaray, reports that appear to have strengthened his standing in negotiations with United's hierarchy.
He captained the side to a hat-trick against Ipswich Town last weekend, a performance that reinforced his importance to Michael Carrick's plans, even if he was unable to inspire United to victory in Sunday's 2-2 draw at Everton.
United's dressing room has reportedly drawn favourable comparisons between Fernandes' influence and Rashford's uncertain path back into the fold following his unsuccessful loan spell at Barcelona last season.
"The lads weren't sure what to expect from Marcus," the source added. "But he's impressed them with his attitude and hard work. They also think he has got better."
Fernandes has established himself as one of the club's most important players since arriving from Sporting CP in January 2020, contributing well over 100 goals and assists in his time at Old Trafford and winning the Professional Footballers' Association Players' Player of the Year award last season.
With his current deal running down and interest from elsewhere clearly present, United's squad appear determined to see the captain's commitment matched by a financial package befitting his standing, both in the dressing room and within the wider Premier League.