The Dutch ace has made a huge impact in Glasgow since joining the Hoops from Groningen over the summer, which has caught the attention of the Premier League giants.
Both clubs have been monitoring the 22-year-old closely in recent weeks, and have been impressed by his mature displays in the Scottish top tier.
Van Dijk – a Dutch U-21 international – was snapped up for just £1.6m last year, but Celtic are said to see him as worth at least £10m now.
However, this figure has not deterred City and Arsenal, who are both extremely interested in the cultured centre-back.
Bhoys boss Neil Lennon is aware of interest in his star, and has backed him to graduate to Holland’s senior set-up on the back on the displays he has been turning in in the green and white shirt:
“It’s inevitable (interest in van Dijk’s signature),
“If he keeps going and progressing the way he is, that he’ll become a Dutch international.”
Arsenal and City could make moves before the close of the current window, but end of season swoops appear to be more likely.