Leadership duties, it is understood, could be handed to British and Irish Lions Test lock Alun-Wyn Jones for a game that sees Wales targeting a successful Six Nations title defence and destroying England's Grand Slam dream in the process.
Sam Warburton, who lost the skipper's role to back-row colleague Jones when he was injured for last month's Paris appointment with France, is viewed in many quarters as an obvious choice.
But with prop Gethin Jenkins also in the mix if he is recalled instead of Paul James, Wales boss Rob Howley might decide on naming a third different captain of the campaign.
Asked about the captaincy, Wales assistant coach McBryde said: "That will be up for discussion.
"There are quite a few sore bodies at this stage after Saturday, and we are not under any pressure to make any decisions at the moment.
"We will take our time and make sure the decisions are right in order to get things spot-on for Saturday.
"We are in a good place. Those decisions will come on Thursday."
Warburton, skipper in the opening Six Nations game against Ireland, was man-of-the-match at Murrayfield last weekend when Wales brushed aside Scotland 28-18.
It was a brave, but totally vindicated, call by Howley not to reinstate him as captain, letting the 24-year-old concentrate solely on his own performance without distractions, and Warburton duly delivered an immense display.
With England breakdown specialist Chris Robshaw offering a significant test for Warburton on Saturday, it could be that Howley decides on a repeat approach.
Alun-Wyn Jones has only led Wales once before - the 2009 Six Nations game against Italy in Rome that produced a 20-15 victory - but he is a natural leader and showing imperious form following his recovery from shoulder surgery earlier this season.
Howley's team announcement is scheduled for Thursday lunchtime, but the absence of 73 times-capped Jones - who is set to be replaced by Justin Tipuric - will hit Wales.
Jones, 32 on Wednesday, led Wales to successive away wins against France, Italy and Scotland, reviving a campaign that could easily have fallen away quickly following an opening weekend home loss to Ireland.
But a shoulder injury suffered during the second-half at Murrayfield now threatens to sideline him until early May.
"Ryan has broken a bone in his shoulder," McBryde added.
"At the moment, it is between six to eight weeks out, so it is not the best of news for Ryan, considering how vital a role he has played for us.
"We are fortunate we have got a bit of strength in depth in the back-row. There is the back-row that finished on the weekend against Scotland, and we've got Aaron Shingler, James King and Andrew Coombs to fall back upon.
"We will sit down as a coaching group and go through all the different permutations."
Jenkins, meanwhile, trained on Tuesday as he continued his recovery from a calf muscle problem that sidelined him for the Scotland game, and McBryde said: "We will be weighing up our options - the strengths of both players (Jenkins and James).
"We are on the back of two very strong scrummaging performances against Italy and Scotland, where both players have figured."
A seven-point victory over England would be enough for Wales - provided they stay ahead of the unbeaten tournament leaders on overall try-count - to secure a second successive Six Nations crown.
A win or draw would be enough to deny England their first Grand Slam since 2003, but on four previous Six Nations occasions Wales have managed to beat their arch-rivals by seven points or more.
"We are focussing on getting our performance right, getting that accuracy in the opening exchanges and not letting the occasion get too big," McBryde said.
"For us, it will be another day at the office. The game will unfold and the game will take care of itself.
"We've given ourselves a chance. It (the title) is not out of our reach, but first and foremost it is about winning those one-on-one battles - the breakdown, the set-piece. You break the game down.
"We've recovered well after a slow start against Ireland, and hopefully we can keep going from strength to strength."
The scrum contest on Saturday will be crucial to the outcome, and after a frustrating penalty-fest in that area at Murrayfield, McBryde hopes for a gripping tussle.
"As a forwards coach, I am as fed up as everyone else with regards to the number of reset scrums going on," he added.
"Hopefully, we will see a good contested area at the scrum and it will be a good spectacle for the spectators.
"All I can say is that we are very proud of the way we have gone about things. We have addressed the issues we had at the start of the campaign, and reaped the benefits in the last two games.
"England have a quality front-row and strength in depth. It is not going to be easy, and we will have to be at our best."