The Express cited an anonymous source at BBC America who spoke of possible love interests for the thirteenth Doctor. While there are no such plans for Series 11, the source mentioned a possible future storyline:

“…the suggestion of this timelord ‘fancying anyone’ is off the table, although there are early plans to introduce an alien who may have enjoyed a relationship with her that is, of course, complicated.”

“The Beeb’s top brass are keen to steer away from having any sexual undertones and the show team are very keen to keep the element of overt sexuality out of this first series.”

Admittedly, it’s a bit early yet to speak of Series 12 storylines before Series 11 airs, but the source alleges concern over a “potential public backlash” will push any romantic involvement for the thirteenth Doctor forward to future series.