The pair go head-to-head on Tuesday when Evans' side open their latest Champions League campaign against Scottish champions Rangers at Old Trafford.
Whilst Evans has been quietly establishing himself as a regular member of Sir Alex Ferguson's starting line-up in the absence of Rio Ferdinand, Davis has resurrected his career with Rangers after falling out of favour at Fulham.
As the club Davis supported as a boy, the Glasgow giants would appear to be the ideal place for the 25-year-old.
However, Evans does not think it will be long before the Ballymena-born star, who started his career at Aston Villa, will be attracting admiring glances from south of the border again.
"Steve is technically and physically one of the best midfielders I have seen coming out of Northern Ireland," said Evans.
"He has fantastic ability and the Rangers fans love him.
"He started off brilliantly at Villa but it did not quite work out for him at Fulham.
"However, he could definitely play for a Premier League team."
Another international colleague of Evans', striker-turned-wide man Kyle Lafferty, will stand in United's way, although the hosts are overwhelming favourites to start their new European adventure with a win.
Wayne Rooney is expected to return after his surprise omission from Saturday's disappointing draw at Everton, with Ferdinand also in contention to shore up a defence that threw victory away by conceding two injury-time goals at Goodison Park.
That ending made Ferguson cross, just as defeat to Bayern Munich in the Champions League last season, when United again appeared to have victory in their grasp, left a sour taste in the Red Devils camp.
One goal ahead from the first minute in Germany, United conceded twice in the latter stages.
Then, having seized the initiative at Old Trafford with a mesmerising display, a combination of a soft Ivica Olic goal and Rafael's dismissal either side of the break turned the tie on its head.
Arjen Robben eventually scored the goal that took Bayern through, to United's total disbelief.
"When we look back at the Champions League last year we still are disappointed," admitted Evans.
"We were in control against Bayern Munich, even away from home because of the early goal we scored.
"But some moments of madness cost us.
"If we had have beaten Bayern Munich we would probably have gone on to win it."