The county attempted to sign the Australian fast bowler Andrew Bichel as a replacement for his Queensland team-mate Michael Kasprowicz, who pulled out of a two-year deal on Monday, citing heat exhaustion.
However, Bichel, who withdrew from last year's Ashes tour through injury, rejected their offer, and Hampshire may now turn to McLean and Dillon.
Malcolm Marshall, the Hampshire and West Indies coach, knows the pair well, and Dillon played for the Southampton club Trojans and the county's second XI two years ago.
The captain, Robin Smith, said: "I've been in touch with Malcolm and also our former captain Mark Nicholas to see what they think. But we're hoping to make an announcement soon, because the new season is just around the corner."
The richest prize in English domestic cricket of pounds 100,000 will be awarded to the winners of this season's County Championship. The sponsors Britannic Assurance have raised the first prize by pounds 30,000 compared with last year, part of their increases announced yesterday.
The runners-up will get pounds 45,000 as against pounds 32,000 in 1997. Third place wins pounds 22,000 and fourth earns pounds 15,000.Reuse content