New Saints boss Stuart Gray is wasting little time in getting his cheque book out and is believed to have lodged a bid of around £4 million - a club record.
Smith has revealed that the club will consider the bid at a board meeting and take things from there, but it seems likely that it will be accepted.
The Republic of Ireland international is already thought to have held brief discussions with the South Coast club and he could very well become The Saints` second signing of the summer after the arrival Swede Anders Svensson.
Southampton currently only have Jason Dodd and youngster Chris Baird in the right back area and Delap could provide cover in defence as well as in the midifeld and striking departments.
When asked Gray would only say: "He [Delap] is one of a number under consideration."
Middlesbrough had long been tipped to make a bid for Delap and could yet make an offer, but their interest in Bordeaux full back Francois Grenet seems to be Steve McClaren`s priority at right back.
Meanwhile, Fabrizio Ravanelli looks set to complete his protracted move from Lazio to Derby next week, after talking with former Rams ace Stefano Eranio.
"I have been on holiday with Stefano and he has convinced me to cut my wage demands so that I can join Derby,‚Ç¥ said Ravanelli.
"Both Stefano and my former Lazio coach Sven Goran Eriksson speak highly of Derby as a club and Jim Smith as a manager.
"I was very impressed when Mr Smith flew to Rome to talk to me and I have viewed the facilities at Pride Park, which are excellent.
"I should like it now if the transfer can be pushed through in time for me to be with the players for pre-season training. That would be to everybody's advantage.
"I feel Derby are a club with some prospects and I can help them. I believe they possess a current squad better than the one I appeared in with Middlesbrough."
