Transfer Gossip: Pompey chasing League Two striker
According to Gloucestershire Live, Kenny Jackett has his eye on the Sudan-born talent.
But Eisa has also attracted interest from the likes of Paul Cook's League One champions Wigan and promotion-chasing Rotherham, as well as a number of Premier League and Championship clubs.
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Hide AdThe 23-year-old has completed his maiden season in the Football League and was a big hit.
He scored 23 goals for the Robins in League Two, finishing as the division's joint-second top goalscorer, along with former Blues striker Marc McNulty.
However, the former Dartford marksman likely won't come cheap.
He's under contract at Whaddon Road until 2020 and is valued at around £1.5m by chairman Paul Baker.
There has reportedly been one verbal offer made for Eisa from a League One club but it falls well short of Cheltenham's asking price.