Choose your moment
Pick a calm, unhurried time, not the middle of a crisis or a busy family gathering. A walk or a cup of tea tends to go better than a formal sit-down.
Start with them, not the problem
Ask what they enjoy, what they'd like to keep doing and what they find tiring. Starting there keeps the conversation about their life, not their limits.
Listen for what matters
Worries about cost, privacy or strangers in the house are common and fair. Listen before you answer. Often the real concern isn't the help itself but what it might mean.
Start small
Help with one thing, such as company, the shopping or a lift to an appointment, is easier to accept than a big change. It can grow from there if they want it to.
Offer a trial, not a decision
"Let's try it once and see" is far easier to say yes to than "you need this now". If it isn't right, nothing is lost.
Keep them in charge
Let your parent choose the days, the activities and, where possible, the person. People accept help more readily when they're steering.
If the answer is no, for now
That's allowed. Leave the door open, check in again in a few weeks, and keep the details handy for when they're ready.