United moved swiftly to appoint Carrick as interim head coach following the dismissal of Ruben Amorim after a turbulent 14 months in charge. While Ruud van Nistelrooy was interviewed, the decision ultimately came down to Solskjaer and Carrick, with club officials backing the latter due to his on-pitch coaching influence.
Carrick enjoyed a dream start, guiding United to a 2-0 derby win over Manchester City. After the victory, Solskjaer reached out to congratulate his former team-mate.
"We're close, we've been through a lot together," Carrick said. "He was fully supportive, wished us all the best and was happy with the result. I've got huge respect for him and he's there if I ever need him."
United now face a tougher challenge away to Premier League leaders Arsenal, where they have lost on their last four league visits. Carrick insists last weekend's win offers belief rather than a tactical template.
"Every game's different," he said. "It won't be copy and paste. We've got to build on what we've done and add new elements. If we're at our best, we feel we've got a good chance."
The trip to north London comes amid confirmation that Casemiro will leave United at the end of the season. Carrick acknowledged he will be involved in discussions around reshaping the squad, particularly in midfield, as the club plans its next steps.