The 24-year-old feels he does not play enough games at Manchester United, where he is currently behind Robin Van Persie and Wayne Rooney in the pecking order.
And Real Madrid think the Mexican, who has 15 goals from 26 appearances this season, would fit in instantly at the Bernabeu.
Whether that move would benefit Hernandez is anyone's guess - Jose Mourinho is not expected to remain in charge of the club into next season, and with Karim Benzema and Gonzalo Higuain already at the club, it is debatable whether Hernandez would play any more football in Spain than he currently does for the Red Devils.
Sir Alex Ferguson is not thought to want to sell him, either - but if his planned move for Borussia Dortmund's Robert Lewandowski comes off in the summer, he may be more receptive to Real's approaches.
Elsewhere Darren Bent may well find himself moving on from Aston Villa, and joining the likes of Wesley Sneijder and Didier Drogba at Turkish giants Galatasaray.
The 29-year-old has been marginalised by Villa in a desperate season, and Galatasaray have shown interest in the striker in the past, say The Sun.
There's an interesting battle brewing between Everton, Liverpool, and Tottenham for a pair of Feyenoord defenders, with all three clubs keen to bring Stefan de Vrij and Bruno Martins Indi to the Premier League. It may cost the winning bidder around £25m, report the Mirror.
The Sunday Telegraph continue to link Edinson Cavani with a move to Manchester City - that may involve, add the Sunday Express, activating his release clause with a £54m offer. But the deal would come because it has been conceded at the Etihad that Radamel Falcao will not be coming, with Chelsea or Real Madrid more likely destinations.
And in news that will hardly set the pulses of England fans racing, Fabio Capello is quoted in The Sun saying he would welcome the chance to manage in the Premier League.
The 66-year-old is currently in charge of the Russian national team, but despite four wins from four qualifiers has reportedly not settled well into life in Russia.