With City manager Gary Mills having offered the 23-year-old Australian new terms, he is too young to leave Bootham Crescent on a free transfer.
Potential suitors would, therefore, need to pay the Minstermen a transfer fee should Meredith decide his future lies elsewhere.
In that scenario, the price would be decided by tribunal if the two parties cannot agree a price but Mills is hoping to avoid that situation.
Having watched the former Telford left-back star in the centre of defence again during Saturday’s season-ending 1-1 draw at Blue Square Bet Premier champions Crawley, the Minstermen chief said: “He was outstanding on Saturday and he is one that I have made an offer to.
“I’m waiting for an answer from him and I hope he’s going to say ‘yes’ because he’s got better and better. When I first came to the club in October, he was clearly an attacking full-back but I thought, defensively, he did not look the finished article in terms of playing at a higher level or being a top-notch player in this division but he learned quickly.
“He’s under 24 so we all know the rules but he enjoys his football here and it’s about me being able to fit him in with my budget along with the other good players we will need for next season.”
Mills insisted that the 2011/12 campaign is already under way in his mind as he prepares to mould a squad capable of finishing champions next term.
He said: “The new season started for me at 7.35pm on Saturday and I’ve got some big decisions to make with a budget that I have to spend right. I’ve got to sign the right players because we’ve finished eighth in the table and I’m disappointed with that even though we have done well considering where we were after a bad start.
“There were expectations at the club and we were not quite good enough so I have to make decisions on the players who will be with me next season and who will come in. I can’t be sympathetic even though I have a group of lovely lads with great attitudes.
“I won’t be rushing into things and, if that means I might lose one or two players because they have other offers, then so be it. I need to be sure in my head that I’ve got the right players with the mental strength to win the league.”
Substitutes Peter Till, Neil Barrett and Greg Young are also not on the books for next season, along with the likes of David Knight, Will Hatfield, David McDermott, Leon Constantine, Michael Gash and George Purcell.
How many have played their last match for City remains to be seen but Mills paid tribute to those on display at the Broadfield Stadium, adding: “Going to Crawley was always going to be tough but the lads did superbly. We showed we wanted to win the game and none of the players let me down.
“They all put 100 per cent in and it took a penalty for them to get a draw with us. Our defence was outstanding and, while I’m not saying the penalty wasn’t a penalty, there were some dodgy decisions that might have had an influence on the result.”
The result meant City finished the campaign with two 1-1 draws against a team who have broken several records on their way to the championship, which Mills hopes bodes well for the future.
He said: “Crawley haven’t beaten us twice and we have won against most of the other teams in the division, as well as setting some records straight against the likes of Newport, Mansfield and Luton. We’ve shown what it takes to beat those sides and I think that’s encouraging ahead of next season.” Crawley striker Matt Tubbs converted a penalty for his 40th goal of the season to earn the hosts a point. Earlier, David Hunt had put through his own net to give City a fifth-minute lead after Fyfield’s cross.
Fyfield played on the left wing after operating at centre-back during the club’s last two games, displaying a versatility that might prove crucial as Mills considers his retained list.
The City boss added: “He looked at home early on in the game and did well for us.”