Says MD Paul Aldridge:
"The deals are progressing for Nigel and Adam and we are hopeful that the everything will be concluded by the end of the week."
Neither player would be available to play for West Ham in the FA cup at Wolves.
Nigel made his first team debut as a substitute against Barnsley on the last day of the 2001-2002 season and has been compared by Dons' boss Stuart Murdoch, who feels he is Premiership class now, with Paul Ince.
The 19 year old product of the Wimbledon youth system turned professional in April 2002 and became a first team regular in the 2002/3 season and was given the captaincy this term.
22 year-old Adam, who signed for around £50,000 from Blackpool in the summer of 2001, took some time to establish himself as a regular with the Dons.
He can play in midfield or as a striker.