The midfielder is the only representative from Ibrox to make an appearance for the national team since the club was voted into Scottish football's bottom tier in the summer.
Strachan was confirmed as Craig Levein's successor earlier this month and Black sees no reason why he would not consider Ally McCoist's men.
He said: "I'm very hopeful. We've got boys like myself and Lee Wallace.
"There are other players in the team - David Templeton is doing well - who are more than capable.
"If we're doing well, I'm sure he won't ignore us."
However, Black admits his own form this season has not been up to scratch so far as he aims to replicate his performances with Hearts last term.
He said: "It's been up and down. I was coming into a good run and I got injured and then suspended.
"I'm just hoping to pick things back up.
"I would love to get the form I was on last year and I'm sure I can get that back.
"It's been tough but I'm enjoying it and I'm sure I'll find the form.
"I've got a lot more to come. I've been really disappointed with my form.
"Coming here, I want to give the best I've got and there's still a lot more that I can give. I just hope I can find it soon."
Meanwhile, Black has become the latest Rangers voice to hit out at league reconstruction plans, with proposals for a 12-12-18 format currently on the table.
If the new structure was approved and implemented for next season, the Scottish Third Division's runaway leaders would remain in the bottom tier regardless of title success.
Black said: "I think for them to change it after the punishment we have taken already, it's basically just another slap in the face for us. "It's right what the Board are saying, that we're playing for nothing so I think they have to look at it.
"If they changed it and we ended up having to stay down here, I just think it is wrong for us."