The influential midfielder has missed the last three games with a badly broken hand but was in the travelling party that set off for south-east London on Monday afternoon.
And although if he plays it will be Robson's first game since he revealed he will be joining MLS side Vancouver Whitecaps in the summer, Mowbray knows he'll be fully committed to the team until then.
"I'm disappointed that the decision has been made by Barry and his family because I saw him as a very important player for us moving forward," said Mowbray.
"But I've had good chats with Barry and if anyone's going to be totally committed, it's him.
"As our supporters know, he plays with his heart on his sleeve and he'll give everything he's got between now and the end of the season and hopefully help us finish strongly."
Boro will need everyone to show plenty of the Robson spirit when they enter the Lions' Den tonight.
Last season's corresponding fixture - pictured above - was held up due to crowd trouble but Boro held their nerve to come out 3-2 winners - and a repeat of that result would do nicely.
"You have to be in there to feel the ferocity from the terraces and how passionate their supporters are for their team," said Mowbray.
"The crowd are right in your face but you know that's coming and that their team will be driven on by that vocal support. You have to match that first and foremost and hope you have some individuals with the talent to help you ask questions of them and win the day."
Kenny Jacket's side sit just three places above the relegation zone and after a 2-0 FA Cup defeat at home defeat to Bolton last weekend will be keen to take a step towards ensuring Championship safety.
Mowbray said: "They'll be disappointed after their defeat to Bolton but they know they have to get back to winning ways and they'll look at the table and see this as an opportunity in front of their own fans to get three points. Our challenge is to make sure they don't.
"It will be a physically and mentally demanding game but hopefully we'll have the tools to try to get the three points."
Former Darlington striker Curtis Main could be involved again after impressing since coming into the squad.
"He seems to have enjoyed his time on the pitch and I'm looking forward to the moment when he gets in front of goal and can show everyone how clinical he can be as well," he said.
"He's got to try to get himself in the starting line-up and then stay there through his performance level and goals. But he's done himself no harm.
Nicky Bailey is edging back towards fitness and although he hasn't travelled to Millwall he could be involved against Reading on Saturday.
"He looks very close and I'd suggest he'll make the 16 for the weekend if he has no setbacks in training," said Mowbray.
"He looks sharp and dynamic but he's had seven weeks of not doing very much. We'll try to get him involved in a game this week and then he has to try to force his way back into what we hope will be a winning team."
Merouane Zemmama is also back training with the first team after his double hernia op but and could be available at the weekend.
*Robson is in the Scotland squad for their friendly in Slovenia on Wednesday February 29 at 8.45pm.
