Wessels averaged 35 with the bat last season
Northants have lost their appeal to retain key players Johannes van der Wath and Riki Wessels.
The pair do not have the necessary working visas as a result of changes to the immigration criteria.
"We are obviously very disappointed that Johan and Riki will be unable to see out their contracts," said Northants chief executive Mark Tagg.
"We have been aware this scenario could happen and head coach David Capel has been looking at alternatives."
South African Van der Wath was Northants' lead bowler last season, taking 50 wickets in the Championship and averaging 25 with the bat.
Johan and Riki have made significant wholehearted contributions to Northants Cricket and the English game
Australian Wessels was first-choice wicketkeeper with a batting average of 35 last season.
Capel said: "Obviously I'm disappointed for the players at the outcome of this appeal.
"Johan and Riki have made significant wholehearted contributions to Northants Cricket and the English game during the past few seasons and given much to the club and its supporters.
"It is necessary to look at all available options open to us, and if we can secure top-class fast bowling expertise that we require to spearhead our attack, it is likely we will be entertaining those options.
"International and other playing commitments could complicate matters further and result in players spending shorter periods of time with us during the 2010 season."