The 34-year-old – whose deal would be subject to ECB approval following last year’s controversial bail-out plan – would be available for the first three months of the season before rejoining his national team for a four-Test series against England in the summer.
Durham are also understood, by ESPNcricinfo, to be mulling over options to replace Cook when he departs, with New Zealand batsman Tom Latham, who has played in the North East Premier League for Gateshead Fell and South Shields, in coach Jon Lewis’s thoughts.
Durham have lost opener Mark Stoneman and No 3 batsman Scott Borthwick to Surrey as they look to rebuild following an enforced relegation to Division Two of the County Championship, hindered by a 48-point deduction too.
Cook has helped South Africa to an unassailable 2-0 lead in their current three-Test series against Sri Lanka on home turf.
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The son of ex-Proteas star Jimmy Cook hit 59 and 117 in the 206-run win in the first Test, thought he was out for nought and 30 in the second Test, won by 282 runs.
In all, he has played eight Tests, scoring 605 runs at an average of 43.21. He averages 41.45 in first-class cricket, from close on 13,000 runs, and has taken 10 first-class wickets, bowling right-arm medium pace.
Durham coach Lewis did not confirm Cook as his overseas target, but told ESPNcricinfo: “We needed the right character. We needed the right quality as a player and the right quality as a person. We have scoured lone and hard and we think we have that now.”