However, the United manager has also stressed that other targets are his priority right now with a couple of prospective deals being “a long way down the line”.
Leeds had an encouraging return to the Championship last season and only missed out on a place in the play-offs by three points.
In an attempt to improve on that seventh-place finish, Grayson wants to strengthen in several key areas – most notably left-back, central defence and in goal, where Kasper Schmeichel is the only player on the books following the release of Shane Higgs.
The impending departure on a free transfer of Bradley Johnson, who is destined for Norwich City, and Hull City target Neil Kilkenny also mean the midfield will have to be bolstered.
Newcastle’s Smith and Woodgate, who earlier this week was released by Spurs, have been linked with a possible return to Elland Road for several months.
Asked if there had been any direct contact, Grayson told the Yorkshire Post: “I have had conversations, though not necessarily with the players themselves. That is how it is in football.
“If anything, it has more been agents ringing me, or people claiming to represent them. There are plenty asking the question and we have to consider it because when good players become available you have to be interested.
“But you have to look at the other side too – finances, injuries and things like that. Like any signing, you have to make sure all the ingredients are right.
“Jonathan has not played too much football and Alan missed quite a bit of last season. If you had a fit Jonathan Woodgate and a fit Alan Smith then you would have a host of clubs queueing up for them in the Premier League.
“The one thing we have got going for us is that they know the club and our ambition. That could help us if we go down that line but there as a long way to go before we even start considering it.
“We are interested in good players but that doesn’t mean those two will necessarily be signing for us. I have got many irons in the fire.
“I am a long way down the line with those other players at this moment in time.”
Leeds are yet to add to their squad this summer despite being linked with a host of names, including Sheffield United’s Nick Montgomery, Neil Danns, of Crystal Palace, and Blackpool midfielder Keith Southern.
Tentative talks are understood to have taken place with Coventry City’s out-of-contract goalkeeper Keiren Westwood but sources in the North East have indicated he will sign for Sunderland.
On the search for new faces, Grayson, who last summer made 11 signings, said: “The transfer market has been pretty quiet, that is the case for most clubs. But we do have irons in the fire and one or two deals are close.
“We have plenty of targets and are speaking to agents and players all the time. It is a waiting game at the moment. Players are trying to get the best deals, while clubs are trying to do the same.
“Eventually, somewhere down the line, you reach an agreement and sign a player. It is not as if we are missing out on targets because not too many clubs are doing any business.
“But I would expect over the next 10 days or so that the market will start hotting up. We still have a bit of work to do. We could have gone out and got half-a-dozen players in the first week of the summer but they wouldn’t have been better than what we have already got.
“We have to be patient. I have also been looking closely at what players have been released by other clubs, who might be available for fees, and who is possibly available in the loan market.
“There are a lot of factors to consider and that is why most clubs don’t do anything really until they get back for pre-season.”
Grayson, speaking at yesterday’s launch of npower’s ‘Search for a Broadcaster’ competition at Beeston Primary School, added: “I won’t put a number on the players I want to bring in. But it won’t be as many as last summer and nowhere near double figures. Then, we needed wholesale changes after winning promotion.
“This time we need a few here and there. I know the positions I want to fill to build on last season. I want more quality than quantity.”
Another Elland Road old boy who has been linked with a possible return is 34-year-old Lee Bowyer, released by Birmingham City.
Grayson said: “Lee Bowyer is another good player and we are aware he is available, as all the other 91 managers in the country will be. We all get the same list.
“But I have not spoken to Lee yet, even though he is a name that keeps being thrown around along with Leeds United.
“I am sure Lee Bowyer will have opportunities in the Premier League. But we have the ambition to match teams from the Premier League, if that is an avenue we choose to go down.”
The publication of the Championship fixtures yesterday means the countdown is under way for the new season.
Grayson said: “Everywhere you look there are good teams in the Championship. But nobody ever said that getting out of the league is easy and we will have a right good go at it.”