The message, seen by Mail Sport, purports to be from the broadcaster's director of sport, Alex Kay-Jelski, and features a statement announcing the former England striker's departure.
Solanke's only previous appearance for England at senior level came in November 2017, shortly after his move to Liverpool.
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The presenter, who earns more than any other BBC star, has been the subject of speculation over his future with the broadcaster for months.
The midfielder was sent off just before half-time in Manchester United 's humiliating 3-0 loss at Old Trafford after scraping his boot against James Maddison 's leg while contesting the ball.
LEWIS STEELE: Sean Dyche had been without England defender Branthwaite (left) for the first four league matches of this term but his return last weekend coincided with their first win.
The game was halted as a result of flares set off by home supporters, with the delay lasting for around a minute.
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Clubs participating in next summer's Club World Cup will have to take their strongest squads and field their strongest teams.
South African Darren Fichardt cards a superb 11-under-par 61 at Kingsbarns to lead by one stroke after day one of the Alfred Dunhill Links Championship.
The South African was one shot clear of Australia’s Cameron John after shooting 61.