Dundee will hold a board meeting today to discuss the future of manager Barry Smith, with the five-man Dens Park board split over whether to allow the 38-year-old to continue in his post.

He was left to talk up the attributes of a team in trouble following a defeat by St Johnstone on Wednesday, referencing the "effort" and "endeavour" which continues to be shown by his side but those words can ring hollow within a boardroom. Some directors are keen for a change in the dugout to try and salvage their season.

Some but not all. The meeting is an attempt to agree on the best way forward and someone such as Jimmy Calderwood – parachuted in to save Kilmarnock and Ross County from relegation in the recent past – might appear an attractive alternative to take charge, although the club may also require an alchemist given they have endured a record of just three wins in the Clydesdale Bank Premier League all season. County are a full nine points ahead of the bottom club and with a game, against Inverness Caledonian Thistle, in hand.

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The statistics will make for dark reading among those charged with deciding Smith's fate today, while they will be aware that some supporters held up a placard demanding his dismissal during the defeat in Perth this week. Such a protest is common among fans aggrieved with poor form but Dundee's Supporters Society is also the major shareholder of the club and so their members will have their voices heard at the board meeting.

Smith had remained philosophical when asked about his future but privately it may jar that he is being sized up for the boot. A former player and youth coach at the club, he took charge of the first team after Dundee fell into administration in 2010 and was a source of strength as he steered them away from relegation to the second division despite having to contend with a raft of departures and a 25-point deduction.

He was also left ill-prepared for a campaign in the top flight as Dundee were belatedly invited to take up the position of Club 12 in the summer as a result of Rangers' financial problems. Some will view talk of his exit as short-sighted and Alex Smith has urged the club to back their manager.

"It would be a PR nightmare if the Dundee board were to sack Barry," said the chairman of the League Managers' Association. "It would be a disgrace. Any reasonable sponsors would walk away which is the last thing they'd want in this current climate.

"It's certainly no way to treat a guy who was a legend as a player and could still go on to be a legend as a manager. Just think back to two years ago when Barry led them out of administration. We're talking about loyalty here at a club which were fighting just to stay alive financially. Now surely that has got to work both ways."

The Dundee board have intimated that there is scope for new arrivals this month, with Colin Nish yesterday officially extending his loan from Hartelpool United until the end of the term. There is a need to address the potentially long-term absence of Stephen O'Donnell, who suffered suspected knee ligament damage at McDiarmid Park, but Smith has not shown any visible signs of pressure to his players.

"He is showing more disappointment and frustration," said Brian Easton, the Dundee defender. "As his players we need to take a lot of the stick off the gaffer. When results aren't going well it seems to be the manager that gets it but I think it is a little unfair."

They are not the only club with one eye on the exit door, with St Johnstone wary of losing players during the transfer windows. Liam Craig is a target of Hibernian and others may attract interest should the Perth side secure a return to Europe this term.

However, Rowan Vine would be happy to agree an extension to his deal before it ends in the summer. "The club can take out an option for next year. I'm happy here," said the striker. "I came here to play and I'm enjoying playing."