Sure:
There are still myriad issues standing between the two countries, most recently their support of opposing sides in the Syrian war. Alliances require shared interests – not just opportunities for temporary cooperation but a long-term convergence on issues of vital importance. Forming new alliances, therefore, requires countries to adopt new interests or, at least, new strategies for pursuing their interests. In the case of Russia and Turkey, there’s little evidence this has happened.
There were myriad issues that stood between Nazi Germany and the USSR allying. There were myriad issues that stood between alliance between the USSR and China. There are myriad issues that stand between alliance between Russia and China. But while those unnatural alliances hold they can cause problems.
The same holds true for Russia and Turkey. And the history of conflict between the two is no longer heightened by bordering each other, sometimes with Turkey (then the Ottoman Empire) well north of their current northern borders. Russia (and the USSR) used to border Turkey in the east and Russia used to have access to Turkey in the west either through compliant or vassal states even when Turkey's border was not pushed north.
[I removed the map from the linked article that I originally inserted because it stopped displaying for some reason.]
So a Russia that would like to break NATO's hold on the Turkish Straits might want to ally with Turkey just to achieve that.
And so a Turkey that would like to expand back into its old Ottoman Empire expanse (in influence if not territory) might want to ally with Russia who would be more cooperative than America.
And both increasingly dictatorial states might see common interests in resisting the perceived threat of American democracy to their systems.
In the long run, a Russian-Turkish partnership might not last long. But in the short run it could be a huge problem. Assuming Turkey isn't just reaching out to Russia to get a better deal with America, as Geopolitical Futures raises. That's normal behavior for smaller states despite Erdogan's dangerous path.
But keep in mind that enduring histories of warfare can end. Britain and France had a long history of warfare--until they became allies. France and Germany had an enduring history of warfare. Until they didn't. America and Britain had a history of warfare and hostility that lasted over a century before reversing into a "special relationship."
So the enduring history of warfare isn't necessarily predictive of whether Russia and Turkey might ally.
And then there is the chance that Turkey going from an ally of America in NATO to an unsteady ally of Russia would only be a transition to Turkish alliance with China to gain a distant ally--and their military technology--against both traditional foe Russia and America which can be expected to oppose Turkish neo-imperial ambitions..
Which neither Russia nor America would like much. If the Russians had any sense at all they'd end their pointless hostility to America and NATO to turn European Russia into a safe rear zone to oppose Turkey and China who could combine to push Russian influence out of Central Asia.
UPDATE: Russia would like to have the Montreux Convention which governs access through the Turkish Straits keep NATO ships out of the Black Sea while allowing Russian naval power to have access to the Mediterranean Sea.
The 21st Century Eastern Question rages.
