Southampton manager Claude Puel could be tempted to play his young star on the biggest stage.
Hesketh was substituted before half-time in Southampton's Europa League tie against Hapoel Be’er Sheva.
The 20-year-old academy product netted his first goal for the club in yesterday's 2-0 win over Crystal Palace.
Jake Hesketh and Harrison Reed came in for praise from the Saints boss.
Manchester United are said to have been tracking Southampton's Jake Hesketh for some time.
Morgan Schneiderlin, who has been linked with a move to Tottenham Hotspur, could feature for Southampton against Sheffield United in the League Cup tomorrow.
The 18-year-old started the 1-0 loss against Burnley this afternoon.
Southampton players and manager Ronald Koeman took to Twitter to react to the club's 2-1 defeat against Manchester United.