He played more than 250 games for the club and made 12 appearances for Wales.
After retiring as a player Nurse invested in property in the city and emerged as a key character in saving the club from insolvency in 2002.
He led the consortium that acquired the the Swans from then-owner Tony Petty.
In addition to their financial problems Swansea were struggling in the bottom tier of the Football League, but have since climbed through the divisions and are in their fifth season in the Premier League.
Nurse stood aside before the club’s meteoric rise.
Swansea’s success means the value of shares is understood to have increased tenfold since the current board took charge in 2002, with the club now valued at about £100m.
More than 70% of the shares are currently held by supporters and directors from south Wales.
Swansea’s directors have been impressed by Levien and Kaplan’s plans, with chairman Huw Jenkins stating when news of the takeover first broke that additional investment would help the club “progress both on and off the field”.
Levien, the managing general partner of Major League Soccer side DC United, has been in Wales for discussions
He and Kaplan, principal of Oaktree Capital investment fund and vice-chairman of NBA franchise Memphis Grizzlies, had initially been negotiating a deal which would have seen them acquire more than 75% of Swansea’s shares.
That would effectively have given the American consortium complete control, including the power to issue more shares.
However, the modified acquisition of 60% will see the trust retain its 21.1% stake and ensure continuity at board level with the retention of Jenkins and vice chairman Leigh Dineen.
They hope to complete a deal before the end of the Premier League season.
*Martin Morgan resigned from his post as a director of OTH Ltd on 4 April 2016
**Brian Katzen and Jeffrey Crevoiserat own one more share than the Swansea City Supporters’ Trust, giving them less than 0.1% more of a share.