But the former Lincoln and Huddersfield chief has also attracted interest from Charlton following yesterday's departure of Lee Bowyer.
The News understands that Cowley and his brother Nicky have been approached to take charge of the Blues for the remainder of the season following the departure of Kenny Jackett.
The length of the contract is somewhat of a concern for the 42-year-old, who has been out of work since July.
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However, the prospect of managing a club the size and with the potential of Pompey also excites.
Cowley has kept tabs on the Blues' League One promotion push this season and previously backed them to finish in the top two.
The London-born chief believes there is a lot of talent in the current squad despite their poor run of just one league win in seven games, which has led to Pompey dropping out of the play-offs.
Cowley feels he and Nicky – his long-time assistant – could galvanise the current group with a fast, attacking brand of football and back their ability.
However, like Daniel Stendel – who's also a candidate to take the Fratton Park hot seat – a short-team deal for the final 13 games of the campaign has only been discussed, which is a sticking point.
What's more, the former PE teacher has also been sounded out by League One rivals Charlton. They're on the lookout for a replacement for Bowyer, who resigned yesterday and is reportedly set to take charge of Birmingham.
Cowley's meteoric managerial rise has been well documented. Having been in charge of non-league Concord Rangers and Braintree, his journey took him to Lincoln in 2016 where he made his reputation.
He guided the Imps back to the Football League in his first season, as well as reaching the FA Cup quarter-finals when they famously beat Premier League Burnley before losing to heavyweights Arsenal.
Cowley then took Lincoln to League One before he left for Championship Huddersfield in September 2019.
He was tasked with keeping the Terriers in the second tier. He arrived with the club sitting second bottom of the table after collecting just one point in their opening six games of the campaign.
Cowley steered Huddersfield clear of the drop yet was sacked with one game remaining. The Yorkshire outfit ended up finishing 18th.
The former Wimbledon youth player was considered for the Sunderland job earlier this season before they appointed Lee Johnson.
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