The 28-year-old has been away from Old Trafford since losing his place under former United manager Ruben Amorim as he continues to flourish at Barcelona on loan.
Having registered 13 goals and 10 assists in 45 competitive appearances, the England international has established himself as one of the best wingers in Europe under manager Hansi Flick.
Barcelona have an option to make Rashford's move permanent for approximately £26M but are reluctant to pay the fee as the summer approaches.
Now, speaking to talkSPORT Bet Casino, McCoist has suggested that Rashford stay in the Premier League and head to North London.
“Rashford could thrive at Arsenal, but they’d have to offload first. The right-hand side of the attack, I'm thinking about Madueke, Saka, you throw in Martinelli, Trossard on the left.
“100 per cent I could see him playing there, yeah. But if I was Rashford, I'd probably want him to think about staying where I am at the moment. I don't know what the deal is, Hansi Flick has been very complimentary about him, and he's done well when he's come in, goal returns good, assists good.
“ So would it be a good move for Arsenal? Yeah, but you need to offload. But if I'm Rashford, I'm going to stay where I am. Especially given he’s going to win the league.”
Rashford has scored three goals in his last four La Liga appearances and could be on the radar for Arsenal boss Mikel Arteta as the likes of Noni Madueke and Bukayo Saka struggle for goal contributions this season.