The glaring and most obvious reason to re-sign Morneau is 'why not?' Neither of the Chris's (Parmelee and Colabello) have shown they deserve the first base spot in 2014 and there aren't any other options on the farm. Morneau is the best current option and, despite age, has the most upside. Furthermore, Mauer's inevitable switch from catching looks more and more distant by the day. First base is basically wide open for Morneau.
So what? Why pay a 32 year old with middling production (.267/.327/.436 for 2012-2013) $5 million or more? Most of the time I'd agree with you, I'd much rather see the money go towards an international free agent or perhaps a starting pitcher on the market.
I think this case is different, I think Morneau might be closer to the all-star level of play we saw from 2006-2010. I know, I know, one month does not a good hitter make. BUT I have a larger argument than that! Morneau has had hot streaks before, take July and August of 2012 in which he hit for an .850 OPS or this May/June when he hit above .300. Why should his latest hot month be any different?
For one reason, in those months he was 'hot' in the sense that he had a pretty batting average but still lacked the power you would expect from a first baseman. Despite what you may have thought, Morneau never was a premier hitter but it's fair to expect 25 round-trippers per year and he's barely approached those modest expectations. This August, however, he's launched seven bombs in 88 plate appearances - a 57 home run pace. His seven homers are also a monthly high since July of 2009. And that's not all, he'd also be on pace for 49 doubles. All this while hitting .294 supported by a very sustainable .295 babip.
It's impossible (and let's be honest, stupid) to say that he's going to be Chris Davis clone for the rest of the season. But the one major missing component from Morneau's game since his 2010 concussion has been his ability to hit for extra bases, as his batting averages have been above average and his defense is still something of an asset at first base. This season he's already just one XBH shy of his 2012 total in 62 fewer plate appearances. If Morneau's power surge is a harbinger of his power ability returning, he's a valuable middle of the order bat and could probably net some serious value in a trade next July ;)
Now the question is, how legit is the newly returned power stroke? Again, only time will tell, but it seems like he's hitting the ball hardly both subjectively (the feeling I get watching the games) and objectively - his 24.1% HR/FB is his highest in any month since July 2010 and four of his seven homers have been classified "Plenty" home runs by ESPN's home run tracker meaning they cleared the fence by more than 10 vertical feet (aka clear home runs). For me, these signs point to Morneau being a 5 HR/Month type of hitter or 30 HR/season.
That is, if he continues to hit the way he's been hitting. Although he hasn't shown this kind of power since his concussion, his other primary foe (besides lack of power) is his inconsistency. So this is where the 'time will tell' argument comes into play. However, if he can ride this streak into the off-season it'll be a great sign for things to come. The final stretch of each season is often ignored by fans because it's difficult for a struggling player to really make a significant impact on his batting average, wOBA or whatever other metric you prefer. However, guys like Jose Bautista, Edwin Encarnacion, Melky Cabrera and plenty of others had their breakout seasons foreshadowed by strong finishes. Perhaps a strong finish from Morneau should be looked at no differently.
EDIT: I completely neglected an Option C: trade him and then re-sign him in the off-season. My worry here is that if he continues raking on a contender, his market will be much hotter this off-season. Rightly or wrongly the market will likely recognize a strong finish from Morneau on a team that is playing meaningful games, if the past is any indication.