Bogdanovic is currently 161st in the world rankings
Great Britain's new Davis Cup captain Leon Smith says Alex Bogdanovic is in line for a recall to the team.
Bogdanovic was axed by former skipper John Lloyd, who lost patience with his repeated failures in live rubbers.
But Smith said: "He's our number two, and our number two by quite a distance, so he has to be in the reckoning.
"If there were four or five players ahead of him, it would be different. Alex is one of the guys that has to be in the mix."
Smith, who is also the Lawn Tennis Association's head of men's tennis, leads GB against Turkey in July.
Defeat in the Europe/Africa Zone Group II play-offs, which start the Friday after Wimbledon, would consign Britain to the lowest rung of the Davis Cup, European Zone Group III.
Andy Murray was coached by fellow Scot Smith as a teenager, but their relationship may not be enough to persuade the British number one and world number four to accommodate the tie in his schedule.
Murray has previously insisted he must put his career ahead of the Davis Cup, and that GB should not have to rely on him to dig them out of trouble.
Speaking on a visit to the French Open, Smith added: "Any country would want Andy to play - [but] if he doesn't, I totally respect that.
"He makes a big difference to the the team, but we've got other players who can come in that are capable of doing the job."