The international side won in Malta in their opening World Cup Qualifier, but have since been held 1-1 at home by Lithuania and beaten 3-0 in Slovakia.
Those results earlier this month saw Strachan’s future as manager widely questioned.
“He was disappointed after the last match, but he knows if he can get a result against England, he’ll never have to buy a drink in Glasgow again. It’s that important to the fans, this is a big match for us.”
Scotland are fourth in Group F, but Regan said: “We’re three matches in, and this group is incredibly tight.
“We’ve seen the performances from teams like Lithuania and, in particular, Slovenia who’ve surprised everybody. We’ve seen Slovakia come back strong against ourselves when we played them recently.
“Anyone can beat anyone else, so we’re determined to get back in amongst it.”