Having seen his chances at Old Trafford dry up and play only a bit-part role at Real Madrid on loan, 'Chicharito' has rediscovered his form in Germany and last season produced a career high tally of 26 goals in all competitions.
According to the Daily Mirror, both English clubs have other priorities in the transfer market this January - Liverpool are said to want a winger, while Spurs are after a creative midfielder - but striker problems for each could prompt a more concerted effort to land Hernandez.
That means attempting to move for the Mexican international, who is also thought to be a potential target for Valencia, sooner rather than later.
It is alleged that the La Liga side are even willing to offer the player's full £33.5m release clause. Whether Spurs or Liverpool would be prepared to pay anything like that amount, which is close to transfer record territory for both clubs, remains to be seen.
Given Hernandez's close relationship with Manchester United fans - he is still fondly remembered at Old Trafford - it is also debatable that he would actually accept a return to the Premier League with a direct rival of his former club and throw that all away.
For Spurs, landing another striker would be a way to provide support for Harry Kane. Vincent Janssen, £17m from AZ in the summer, has verged on hopeless at times as he continues to try and find his feet in England.
At Liverpool, the arrival of any new forward could spell the end for Daniel Sturridge.
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