The two Premier League giants have been linked with the Dane in the past following an impressive season on-loan with Fulham.
Despite the Whites suffering relegation to the Championship at the end of the campaign, Andersen was a shining light for his consistent performances at the heart of defence.
Now, it has been revealed that the centre-back is set to stay in England, and specifically London.
According to Danish outlet BT, Andersen is “almost certain” to remain in the capital despite his period at Craven Cottage having come to an end.
Arsenal are thought to be interested, whilst managerless Spurs have apparently opened talks with the player’s parent club Lyon over a deal that could potentially cost as much as £19m.
It remains to be seen what side he will be representing heading into the 2021/22 campaign but staying in London, Andersen would be ideally situated to sign for either Arsenal or Spurs.
The 25-year-old still has three years left to run on his most recent contract with Lyon having signed for the French giants from Sampdoria in 2019.
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He made 31 Premier League appearances for Fulham last season having joined the club in October.
The centre-back was recently named in the Denmark squad for the upcoming European Championships that is set to get underway next Friday.
Kasper Hjulmand’s men get their tournament underway with a clash against Finland on Saturday before clashes against Belgium and Russia to conclude the group stages.