The Scotland international missed last weekend's 0-0 draw with Liverpool but is contention to face Ronald Koeman's men after returning to training earlier this week.
However, assistant manager Steve Agnew reveals there is no guarantee wing-back Robertson will play after replacement Robbie Brady put in a fine performance at Anfield, prompting manager Steve Bruce to suggest he would be selected again this week.
"We'll discuss that [team selection] today," Agnew said. "It's a dilemma because Andrew has done so well since coming down from Scotland and really hit the ground running.
"But then Robbie came in last weekend and performed exceptionally well at Liverpool. It's a great problem to have."
Agnew also confirmed that injured quartet Allan McGregor, Steve Harper, Nikica Jelavic and Michael Dawson are all progressing well and could return for the Premier League clash with Tottenham after the international break later this month.
Meanwhile, Agnew insists close-season signing Tom Ince still has a big future at the club despite being shipped out on loan to Nottingham Forest.
Ince has struggled to make an impact at the KC Stadium and, after missing several matchday squads, Bruce allowed the winger to leave on a temporary basis.
"Tom came in pre-season and did ever so well when started the season with us," he added.
"We changed the shape of the team and then one or two players came in or out and Tom was one of those.
"We felt he hasn't played as much football as we would have liked so Steve agreed with Nottingham Forest to take him on loan until January.
"Hopefully he'll get some games in, perform like we know he can and it will be beneficial to all of us.
"He is a top player, an exciting player and one we're looking forward to working with for a good number of years."
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