The report states that Stoke City are also keeping an eye on the centre-back.
A youth product of Ipswich Town, Clarke spent 12 years with the club.
After making a few appearances with the first team, the central defender joined Pompey in 2016 signing a three-year deal.
Since then, he has been a regular for the side and his consistent performances earned the League 2 side a promotion.
The 22-year-old was at the heart of the defence that would go on to concede fewest goals in the league.
He has a year left on his contract with Pompey.
Possibilities of signing
The reports from The Times state that the Englishman could be persuaded for a price around £4 million, which can be afforded by the Peacocks.
With the Whites expected to qualify for the Premier League next season, Marcelo Bielsa will count on his reliable players. Yet he could also look to provide cover for the first choice centre-backs.
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The Elland Road side picked up an important win against Millwall on Saturday and as a result, they have moved to second in the Championship table.
They are currently trailing Norwich City by five points.