API 653 (tank inspection standard) recommends the tank foundation be inspected for cracks/deterioration (Section 4.5) which is typically where vegetation will grow. Additionally, the In-Service Inspection Checklist seen in Appendix C contains a housekeeping line item to inspect for trash, vegetation, and inflammables.
Vegetation is typically found in the secondary containment (dike area around a tank); if the product stored requires secondary containment vegetation may be a warning sign that the containment needs repair.